Question

Without solving the following quadratic equation, find the value of ‘m’ for which the given equation has real and equal roots.

X² + 2(m – 1) x + (m + 5) = 0

Answer 1

Consider the given equation:

X² + 2(m – 1) x + (m + 5) = 0

The nature of the roots of a quadratic equation

ax² + bx + c = 0, depends entirely on the

value of its discriminant b² – 4ac.

If a, b and c are real numbers and a ≠ 0, Then discriminant:

(i) b² −4ac = 0 ⇒ the roots are real and equal

(ii) b² −4ac > 0 ⇒ the roots are real and unequal.

(iii) b² −4ac < 0 ⇒ the roots are imaginary (not equal) 

Since the roots of the given equation are real and equal,

We have,