Quadratic equations are equations of the form ax^{2} + 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 (b^{2} – 4ac))/2a and (-b – root (b^{2} – 4ac))/2a

Here is a typical quadratic equation question

If m and n are the roots of the quadratic equation x^{2} – (2 root 5)x – 2 = 0, the value of m^{2} + n^{2} is:

A. 22

B. 24

C. 32

D. 20

E. 18

Correct Answer is Choice B. 24.

**Explanation**

m and n are roots of the equation.

We have to find the value of m^{2} + n^{2}

m^{2} + n^{2} = (m + n)^{2} – 2mn

(m + n), the sum of the roots of a quadratic equation of the form ax^{2} + 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 x^{2} – (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.

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