Question

Find the value of ‘p’ for which the roots of the following equation are real and equal:

9x² − 24x + p = 0

Answer 1

Given:

9x² − 24x + p = 0

For a quadratic equation ax² + bx + c = 0, the discriminant is:

D = b² − 4ac

For real and equal roots, the discriminant must be:

D = 0

Identify the coefficients

a = 9

b = −24

c = p

D = (−24)² − 4(9) (p)

= 576 − 36p

576 − 36p = 0

36p = 576

`p = 576/36`

p = 16