If the roots of the quadratic equation kx² + (a + b)x+ ab are (-1,- b),What is the value of k?

A quadratic equation is in the form ax² + bx + c = 0, where a ≠ 0.

Answer: If the roots of the quadratic equation kx² + (a + b)x + ab are (-1) and (-b) then the value of k is 1.

Let's see the detailed solution.

Explanation:

-1 and - b would satisfy the quadratic equation if they are the roots of the quadratic equation.

On substituting x = - b in the quadratic equation we get,

k(-b)² + (a + b)(-b) + ab = 0

⇒ kb² - ab - b² + ab = 0

⇒ kb² - b² = 0

⇒ b²(k - 1) = 0, where b ≠ 0

therefore, k - 1 = 0

⇒ k = 1

Thus, If the roots of the quadratic equation kx² + (a + b)x + ab are (-1) and (-b) then the value of k is 1.