Quadratic equations are equations of the form ax2 + bx + c = 0.
A quadratic equation has two roots. These roots are found either by factorizing the quadratic equation or by using the formula (-b + root (b2 - 4ac))/2a and (-b - root (b2 - 4ac))/2a
Here is a typical quadratic equation question
If m and n are the roots of the quadratic equation x2 - (2 root 5)x - 2 = 0, the value of m2 + n2 is:
Correct Answer is Choice B. 24.
m and n are roots of the equation.
We have to find the value of m2 + n2
m2 + n2 = (m + n)2 - 2mn
(m + n), the sum of the roots of a quadratic equation of the form ax2 + bx + c = 0 is (-b/a)
mn, the product of the roots of the equation = c/a
The sum of the roots of the equation x2 - (2 root 5)x - 2 = 0 is (2 root 5).
Product of the roots of the equation = -2.
Hence, (m + n)2 - 2mn = (2 root 5)2 - 2(-2) = 20 + 4 = 24.
Labels: GMAT Quadratic Equations, GMAT Roots of Equations, product of roots, sum of roots