Question

If sum of the roots of the quadratic equation kx2+12x+8k=0 is equal to the product of its roots, then find the value of k.

Answer 1

The sum and the product of the roots of the quadratic equation kx² + 12x + 8k = 0 are equal.

When we compare kx² + 12x + 8k = 0 to ax² + bx + c = 0, we get :

• a = k
• b = 12
• c = 8k

Given that :

• αβ = α + β . . . . . (1)

We know that :

• Product of zeroes (αβ) = c / a

⟹ 8k / k

⟹ 8

• Sum of zeroes (α+β) = - b / a

⟹ - 12 / k

Equating both from (1) :

⟹ 8 = - 12 / k

⟹ 8k = - 12

⟹ k = - 12 / 8

⟹ k = - 3 / 2

➤ Therefore, the value of k in kx² + 12x + 8k = 0 when the sum and product of the roots is equal is - 3 / 2.