Q) Write all the values of p for which the quadratic equation x² + px +16 = 0 has equal roots. Find the roots of the
equation so obtained.

Ans:

We know that in a standard quadratic equation, a x² + b x + c = 0 will have equal roots when its discriminant is 0.

i.e. D = b² – 4 a c = 0

Comparing the given equation x² + px +16 = 0 with standard equation, we get:

a  = 1, b = p and c = 16

For this quadratic equation to have equal roots, its discriminant should be zero.

∴ (p)² – 4 (1) (16) = 0

∴ p² = 64

∴ p =

Therefore for the roots, p = 8 and p = – 8, the given quadratic equation will have equal roots.

Please press the “Heart” button if you like the solution.