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What is the root of equation?
roots of equation are x values when y = 0
If a quadratic equation has roots at 3 and -5 which factors could be multiplied together to obtain an original equation?
(x - 3) and (x - (-5)).
What are the roots of the equation x squared -3x-2 equals 0?
I will use the quadratic equation here. By inspection the discriminant shows 2 real roots. X = -b +/- sqrt(b^2 - 4ac)/2a a = 1 b = - 3 c = - 2 X = -(-3) +/- sqrt[(-3)^2 - 4(1)(-2)]2(1) X = 3 +/- sqrt(17)/2 X = [3 +/- sqrt(17]/2 exact answer.
What are the roots of the quadratic equation 2X2-3X-3 equals 0?
Use the quadratic equation to find the roots of 2x2-3x-3=0.a=2, b=-3, c=-3x =[ -b +- SQRT(b2-4ac)]/2a=[--3 +- SQRT((-3)2 - 4(2)(-3))]/2*2= [3+-SQRT(9--24)]/4so the roots are x = [3+SQRT(33)]/4 and x = [3-SQRT(33)]/4
How do you solve the Relationship between the coefficient and roots of quadratic equations?
TO FIND THE RELATION BETWEEN ROOTS AND COEFFICIENTS OF A QUADRATIC EQUATION:Let us take the general form of a quadratic equation:ax2 + bx + c = 0 (1)where a(≠0) is the coefficient of x2 , b is the coefficient of x and c is a constant term. If and ß be the roots of the equation, then we have to find the relations of and ß with a, b and c.Since a ≠0, hence multiplying both sides of (1) by 4a we get,4a2x2 + 4abx + 4ac = 0 or (2ax)2 + 2.2ax.b + b2 - b2 + 4ac = 0Or, (2ax + b)2 = b2 - 4ac2ax + b = b2 - 4acx =Hence, the roots of (1) areLet, = and ß =Hence, + ß = +Or + ß = = - b/a = - (2)Again ß = xOr ß = =Or ß = = = (3)Equations (2) and (3) represent the required relations between roots (that is, and ß) and coefficients (that is, a, b and c) of equation (1).Example 1:If the roots of the equation 2x2 - 9x - 3 = 0 be and ß, then find + ß and ß.Solution:We know that + ß = - = - =And ß = = (Answer)Example 2:If one root of the quadratic equation x2 - x - 1 = 0 is a, prove that its other root is 3 - 3.Solution:x2 - x - 1 = 0 (1)Let ß be the other root of the equation (1). Then,+ ß = = 1 or ß = 1 -Since is a root of the equation (1) hence, 2 - - 1 = 0 or 2 = + 1Now, 3 - 3 = . 2 - 3 = ( + 1) - 3 [Since 2 = + 1]= 2 + - 3 = + 1 - 2 = 1 - = ß [Since ß = 1 - ]Hence, the other root of equation (1) is 3 - 3. (Proved)Example 3:If a2 = 5a - 3 and b2 = 5b - 3, (a ≠b), find the quadratic equation whose roots are and .Solution:Given (a ≠b) and a2 = 5a - 3 and b2 = 5b - 3, hence it is clear that a and b are the roots of the equation x2 = 5x - 3 or x2 - 5x + 3 = 0.Hence, a + b = - = 5 and ab = = 3.Now, the sum of the roots of the required equation= + = = = = =And the product of the roots of the required equation = . = 1.Hence, the required equation is x2 - x + 1 = 0 or 3x2 - 19x + 3 = 0. (Answer)
How many real roots does the equation 2x2-5x-3 equals 0 have?
2x2 - 5x - 3 = 0 A quadratic equation expressed in the form ax2 + bx + c = 0 has two real and distinct roots when b2 - 4ac is positive. Using the figures from the supplied equation then b2 - 4ac = 52 - (4 x 2 x -3) = 25 + 24 = 49. Therefore there are TWO real and distinct roots.
How many real solutions does a cubic equation have?
A cubic has from 1 to 3 real solutions. The fact that every cubic equation with real coefficients has at least 1 real solution comes from the intermediate value theorem. The discriminant of the equation tells you how many roots there are.
Roots of the equation x 2 plus 5x plus 7 equals 0 will be?
There are no real root. The complex roots are: [-5 +/- sqrt(-3)] / 2
Can bisection method give us two answers for different intervals for same equation i have equation 2x3 plus x2-20x plus 12 equals 0. i have to find real root upto 3 correct decimal places. I chose int?
Yes. A cubic equation can have 3 real roots. Depending on their size, each of three intervals could contain a root. In that case different intervals must give different roots.Yes. A cubic equation can have 3 real roots. Depending on their size, each of three intervals could contain a root. In that case different intervals must give different roots.Yes. A cubic equation can have 3 real roots. Depending on their size, each of three intervals could contain a root. In that case different intervals must give different roots.Yes. A cubic equation can have 3 real roots. Depending on their size, each of three intervals could contain a root. In that case different intervals must give different roots.
What are 3 outcomes for the discriminant?
If the discriminant of a quadratic equation is zero then it has equal roots. If the discriminant is greater than zero then there are two different roots. If the discriminant is less than zero then there are no real roots.
How many roots does a quadratic equation in one variable have?
A quadratic equation has two roots. They may be similar or dissimilar. As the highest power of a quadratic equation is 2 , there are 2 roots. Similarly, in the cubic equation, the highest power is 3, so it has three equal or unequal roots. So the highest power of an equation is the answer to the no of roots of that particular equation.
What is the real sixth roots of 729?
They are -3 and +3.
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 is the root of equation?
roots of equation are x values when y = 0
How many roots does the equation 3 x plus 7 have?
That is not an equation, since it doesn't have an equal sign.
What are 3 other names for solutions of a quadratic equation?
Roots, zeroes, and x values are 3 other names for solutions of a quadratic equation.
What is the answer of 4x2plus9equal12x?
It is a quadratic equation and when solved it has equal roots of 3/2 or 1.5
