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the sum is -b/a
and the product is c/a
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∙ 12y ago
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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 sum of the exterior angles of a 12-gon?
The sum of exterior angles for any figure is 360. If you want the sum of the interior angles use the equation 180(n-2) for n equals number of sides.
Find the sum of the angle measures in a 11-gon?
1620 the equation to find the sum of the interior angles for any regular polygon is: (n-2)x180, where n=the number of sides.
What is the sum of the angle measures of a 17 sided polygon?
Heres a good trick to figuring out the sum of the angles of an "n" sided polygon. It's common knowledge that a triangle (3 sides) has a sum of 180 degrees and a square (4 sides) is 360 degrees. You can infer that a pentagon (5 sides) has a sum of 540 degrees. So the equation to figure out the sum of all the angles of an "n" sided polygon is 180*(n-2). So in your case n = 17 so the equation becomes 180(17-2) = 2700 degrees
What are the lengths of each diagonal of a rhombus when they add up to 11.55 cm and it has an area of 16.335 square cm showing all work with answers?
Let the diagonals be x and y and so:- If: x+y = 11.55 then y = 11.55-x Area: 0.5*x*y = 16.335 => x*(11.55-x) = 16.335*2 So: 11.55x-x^2 = 32.67 => 11.55x-x^2 -32.67 = 0 Solving the above quadratic equation: x = 4.95 or x = 6.6 Therefore by substitution its diagonals are: 4.95 cm and 6.6 cm Check: 4,95+6.6 = 11.55 cm which is the sum of its diagonals Check: 0.5*4.95*6.6 = 16.335 square cm which is its area
Formula of quadratic equation if roots are given?
A quadratic equation has the form: x^2 - (sum of the roots)x + product of the roots = 0 or, x^2 - (r1 + r2)x + (r1)(r2) = 0
What roots of the quadratic equation are equivalent to xx-x-12 equals 0?
-4,3 are the roots of this equation, so for the values for which the sum of roots is 1 & product is -12
What does b represent in a quadratic equation?
b is the negative sum of the roots of the equation
Are there two integers with a product of-12 and a sum of-3?
-9
What is the sum of the roots of the equation -x squared equal to 3x plus 4?
It has no roots because the discriminant of the given quadratic equation is less than zero.
How do you find the sum of the roots of the equation x2 plus 5x plus 9 equals 0?
This quadratic equation has no real roots because its discriminant is less than zero.
What is the solution of a quadratic equation called?
Sum
What is the equation for The product of 5 and the sum of 8 and 2?
find the sum and product of the roots of 8×2+4×+5=0
How do you use a quadratic equation to find two real numbers whose sum is 5 and whose product is -14?
19
How a product and a sum are alike and how they are different?
A product is the answer of a multiplication equation. A sum is the answer of an addition equation.
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.
What can you add to get twenty-seven and multiply to get twenty-one?
If the given information is the sum and the product of two numbers, then the numbers are not integers, because only 1*21 or 3*7 equals 21, and their sum is different from 27. So let's write the quadratic form of an equation given the sum and the product of roots, and solve it. The sum = 27, the product = 21 x2 - (summ of the roots)x + (product of the roots) = 0 x2 - 27x + 21 = 0; a = 1, b = -27, and c = 21 x = [-b ± √(b2 - 4ac)]/(2a) the quadratic formula x ={-(-27) ± √[(-27)2 - 4(1)(21)]/[2(1)] = [27 ± √(729 - 84)]/2 = (27 ± √645)]/2 Thus, the numbers are (27 - √645)]/2 and (27 + √645)]/2.
