Question

If one root of the quadratic equation x² + 12x – k = 0 is thrice the other root, then find the value of k.

Answer 1

Compare quadratic equation x² + 12x – k = 0

With ax² + bx + c = 0

Then, a = 1, b = 12, c = –k

Let first root of given quadratic equation be α

According to question second root = 3α

We know that

Sum of roots = `-b/a`

α + 3α = `(-b)/a`

`\implies` 4α = `(-12)/1`

`\implies` α = –3

Product of roots = `c/a`

α × 3α = `(-k)/1`

3α² = –k

Put the value of α

3 × (–3)² = –k

k = –27