Question

If one root of the equation 3x² + kx + 81 = 0 (having real roots) is the square of the other then find k

Answer 1

Let α and α² be the root of the equation 3x² + kx + 81

Here a = 3, b = k, c = 81

α + α² = `- "k"/3`

3α + 3α² = – k   ...(1)

Product of the roots = `"c"/"a" = 81/3` = 27

α × α² = 27

α³ = 27 ⇒ α³ = 3³

α = 3
Substitute the value of α = 3 in (1)

3(3) + 3(3)² = – k

9 + 27 = – k

⇒ 36 = – k

∴ k = – 36

The value of k = – 36