Question

If -5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x)k = 0 has equal roots, find the value of k.

Answer 1

Given –5 is a root of the quadratic equation 2x² + px – 15 = 0.

∴-5 satisfies the given equation.

∴ 2(5)²+ p(-5)-15 = 0

∴ 50 - 5p - 15= 0

∴ 35-5p = 0

∴5p = 35 ⇒ p = 7

Substituting p = 7 in p(x² + x)+ k= 0,we get

7(x²+x)+k=0

∴7x² + 7x + k = 0

The roots of the equation are equal.

∴ Discriminant b² - 4ac = 0

Here, a=7, b=7, c=k

b²-4ac=0

∴ (7)² - 4(7)(k)=0

∴ 49-28k= 0

∴28k =  49

∴ k = `49/28=7/4`