If the sum and product of the roots of a quadratic equation are 2 and – 100 respectively, then which one of the following is correct?

Correct option is C

Given:

Sum of the roots (S) = 2

Product of the roots (P) = -100

Concept Used:

For a quadratic equation of the form x²+ bx + c = 0,

The sum of the roots (α + β) = -b

The product of the roots (αβ) = c

Formula Used:

x²- (Sum of the roots)x + Product of the roots = 0

Solution:

Using the given sum and product of the roots:

=> Sum of the roots (S) = 2

=> Product of the roots (P) = -100

Substitute into the formula for the quadratic equation:

=> x²- Sx + P = 0

=> x²- 2x - 100 = 0

Thus, the quadratic equation is:

x²- 2x - 100 = 0

Hence, the correct answer is option c.