Question

If the roots of x² – px + 4 = 0 are equal, the value (values) of p is ______.

Options

• 4 and – 4

• 4

• – 4

• 4 or – 4

Answer 1

If the roots of x² – px + 4 = 0 are equal, the value (values) of p is 4 or – 4.

Explanation:

Given quadratic equation be

x² – px + 4 = 0   ...(1)

On comparing equation (1) with

ax² + bx + c = 0

We have a = 1; b = – p and c = 4

Since equation (1) has equal roots

∴ D = 0

`\implies` b² – 4ac = 0

`\implies` (– p)² – 4 × 1 × 4 = 0

`\implies` p² – 16 = 0

`\implies` p² = 16

`\implies` p = ± 4

`\implies` p = 4 or – 4