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There is no sign before 36. However, assuming the missing sign is a plus, the roots are 4 and 9.
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How do you find the values of k when the straight line y equals kx -2 is a tangent to the curve y equals x squared -8x plus 7?
By implication : x2-8x+7 = kx-2 Form a quadratic equation: x2-8x-kx+9 = 0 For a line to be a tangent to the curve it must have two equal roots and the discriminant b2-4ac of the quadratic equation must equal 0. So: (-8-k)2-4*1*9 = 0 (-8-k)2-36 = 0 (-8-k)2 = 36 Square root both sides: -8-k = -/+6 -k = 2 or 14 k = -2 or -14 When k = -2 is substituted into the quadratic equation x will have two equal roots of 3 When k = -14 is substituted into the quadratic equation x will have two equal roots of -3
How many ways are there to solve a quadratic equation?
There are so far 8 common methods to solve quadratic equations:GraphingFactoring FOIL methodCompleting the square.Using the quadratic formula (derived from algebraic manipulation of "completing the square" method).The Diagonal Sum Method. It quickly and directly gives the 2 real roots in the form of 2 fractions. In fact, it can be considered as a shortcut of the factoring method. It uses the Rule of Signs for Real Roots in its solving process. When a= 1, it can give the 2 real roots quickly without factoring. Example. Solve x^2 - 39x + 108 = 0. The Rule of Signs indicates the 2 real roots are both positive. Write the factor-sets of c = 108. They are: (1, 108), (2, 54), (3, 36)...Stop! This sum is 36 + 3 = 39 = -b. The 2 real roots are 3 and 36. No needs for factoring! When a is not one, this new method selects all probable root-pairs, in the form of 2 fractions. Then it applies a very simple formula to see which root-pair is the answer. Usually, it requires less than 3 trials. If this new method fails, then this given quadratic equation can not be factored, and consequently the quadratic formula must be used. Please see book titled:"New methods for solving quadratic equations and inequalities" (Amazon e-book 2010).The Bluma MethodThe factoring AC Method (Youtube). This method is considerably improved by a "new and improved AC Method", recently introduced on Google or Yahoo Search.The new Transforming Method, recently introduced, that is may be the best and fastest method to solve quadratic equations. Its strong points are: simple, fast, systematic, no guessing, no factoring by grouping, and no solving the binomials. To know this new method, read the articles titled:"Solving quadratic equations by the new Transforming Method" on Google or Yahoo Search.BEST METHODS TO SOLVE QUADRATIC EQUATIONS. A. When the equation can't be factored, the best choice would be the quadratic formula. How to know if the equation can't be factored? There are 2 ways:1. Start solving by the new Transforming Method in composing factor pairs of a*c (or c). If you can't find the pair whose sum equals to (-b), or b, then the equation can't be factored.2. Calculate the Discriminant D = b^2 - 4ac. If D isn't a perfect square, then the equation can't be factored.B. When the equation can be factored, the new Transforming Method would be the best choice.
What is the answer to x equals 36?
36=36The "answer" is the number that ' x ' must be in orderto make the equation a true statement.The answer to this equation is: 36 .
What is the slope of a line whose equation is 17x-12y equals -36?
17/12
What is the equation for a circle with the center of -3 -5 and a radius of 6?
It is: (x+3)^2 + (y+5)^2 = 36
What are the two factors of the following equation x plus 13x plus 36?
(x+9)(x+4)
What is x squared plus 13x plus 36 equals 0 factor to?
Well, if that was a - 13X we could factor by inspection, but now the quadratic formula is needed. By inspection the discriminant yields two real roots. X^2 + 13X + 36 = 0 X = - b (+/-) sqrt(b^2-4ac)/2a a = 1 b = 13 c = 36 X = - 13 (+/-) sqrt[b^2 - 4(1)(36)]/2(1) X = - 13 (+/-) sqrt(169 - 144)/2 X = - 13 (+/-) sqrt(25)/2 X = [- 13 (+/-) 5]/2 X = - 4 ------------ X = - 9 -----------
Factor x2 plus 13x plus 36 completely?
x2 + 13x + 36 = (x + 9)(x + 4)
How do you find the values of k when the straight line y equals kx -2 is a tangent to the curve y equals x squared -8x plus 7?
By implication : x2-8x+7 = kx-2 Form a quadratic equation: x2-8x-kx+9 = 0 For a line to be a tangent to the curve it must have two equal roots and the discriminant b2-4ac of the quadratic equation must equal 0. So: (-8-k)2-4*1*9 = 0 (-8-k)2-36 = 0 (-8-k)2 = 36 Square root both sides: -8-k = -/+6 -k = 2 or 14 k = -2 or -14 When k = -2 is substituted into the quadratic equation x will have two equal roots of 3 When k = -14 is substituted into the quadratic equation x will have two equal roots of -3
How do you factor X squared minus 36?
This is a basic quadratic equation. The question must be regarded as, How do you factor x² - 36 = 0 ? This equation can be written as x² - 6² = 0, which factors as (x + 6)(x - 6) = 0 This leads to the solutions (or roots) x = -6 and x = 6, often written as x = ±6
Factor completely X2-13x plus 36?
if you mean x^2-36 1x^2+0x-36 a=1 b=0 c=-36 you can use quadratic formula (-b -+ sqrt (b^2-4ac))/2a you'll get (sqrt(144))/2= 6 and (-sqrt(144))/2= -6 as your two roots your answer (x+6)(x-6) or use inspection: what factors of c will give you b when added together if c=-36 and b=0. the roots 6 and -6 will get you 0 when added and -36 when multiplied. because 6 and -6 are your chosen factors the factored expression is (x+6)(x-6)
What two numbers have a sum of 13 and a product of 36?
Let your numbers be x and y So you can write the equations... x+y=13 and xy=36 Solving the first equation you get y=13-x Using substitution (plugging the equation above into the second equation) x(13-x)=36 13x - x^2 = 36 Set your equation equal to zero... x^2 - 13x + 36 = 0 Factoring... (x-9)(x-4)... so, x=9 and x=4 Plugging these values back into your original equations gives you that one of your answers is 9 and the other is 4.
What is the special cases of quadratic equation?
The standard form of a quadratic equation is: ax^2 + bx + c = 0. Depending on the values of the constants (a, b, and c), a quadratic equation may have 2 real roots, one double roots, or no real roots.There are many "special cases" of quadratic equations.1. When a = 1, the equation is in the form: x^2 + bx + c = 0. Solving it becomes solving a popular puzzle: find 2 numbers knowing their sum (-b) and their product (c). If you use the new Diagonal Sum Method (Amazon e-book 2010), solving is fast and simple.Example: Solve x^2 + 33x - 108 = 0.Solution. Roots have opposite signs. Write factor pairs of c = -108. They are: (-1, 108),(-2, 54),(-3, 36)...This sum is -3 + 36 = 33 = -b. The 2 real roots are -3 and 36. There is no needs for factoring.2. Tips for solving 2 special cases of quadratic equations.a. When a + b + c = 0, one real root is (1) and the other is (c/a).Example: the equation 5x^2 - 7x + 2 = 0 has 2 real roots: 1 and 2/5b. When a - b + c = 0, one real roots is (-1) and the other is (-c/a)Example: the equation 6x^2 - 3x - 9 = 0 has 2 real roots: (-1) and (9/6).3. Quadratic equations that can be factored.The standard form of a quadratic equation is ax^2 + bx + c = 0. When the Discriminant D = b^2 - 4ac is a perfect square, this equation can be factored into 2 binomials in x: (mx + n)(px + q)= 0. Solving the quadratic equation results in solving these 2 binomials for x. Students should master how to use this factoring method instead of boringly using the quadratic formula.When a given quadratic equation can be factored, there are 2 best solving methods to choose:a. The "factoring ac method" (You Tube) that determines the values of the constants m, n, p, and q of the 2 above mentioned binomials in x.b. The Diagonal Sum Method (Amazon ebook 2010) that directly obtains the 2 real roots without factoring. It is also considered as "The c/a method", or the shortcut of the factoring method. See the article titled" Solving quadratic equations by the Diagonal Sum Method" on this website.4. Quadratic equations that have 2 roots in the form of 2 complex numbers.When the Discriminant D = b^2 - 4ac < 0, there are 2 roots in the form of 2 complex numbers.5. Some special forms of quadratic equations:- quadratic equations with parameters: x^2 + mx - 7 + 0 (m is a parameter)- bi-quadratic equations: x^4 - 5x^2 + 4 = 0- equations with rational expression: (ax + b)/(cx + d) = (ex + f)- equations with radical expressions.
What are examples of quadratic formula with 2 imaginary roots?
A quadratic equation has the form: x^2 - (sum of the roots)x + (product of the roots) = 0 If the roots are imaginary roots, these roots are complex number a+bi and its conjugate a - bi, where a is the real part and b is the imaginary part of the complex number. Their sum is: a + bi + a - bi = 2a Their product is: (a + bi)(a - bi) = a^2 + b^2 Thus the equation will be in the form: x^2 - 2a(x) + a^2 + b^2 = 0 or, x^2 - 2(real part)x + [(real part)^2 + (imaginary part)^2]= 0 For example if the roots are 3 + 5i and 3 - 5i, the equation will be: x^2 - 2(3)x + 3^2 + 5^2 = 0 x^2 - 6x + 34 = 0 where, a = 1, b = -6, and c = 34. Look at the denominator of this quadratic equation: D = b^2 - 4ac. D = (-6)^2 - (4)(1)(34) = 36 - 136 = -100 D < 0 Since D < 0 this equation has two imaginary roots.
How do you solve x2-13x plus 36 equals 0 for x?
x2-13x+36=(x-9)(x-4)=0 x=9 or x=4
What is the discriminant for x2-4x-5 equals 0?
The discriminant is 36 which means the quadratic equation has two solutions which are 5 and -1
What is x squared plus 5x minus 36 equals 0?
It is a quadratic equation and its solutions are: x = 4 or x = -9
