The roots of the equation ax² + x + b = 0 are equal if

Question

Question

Answer 1

Given:

The given equation is ax² + x + b = 0

Concept used:

General form of the quadratic equation is ax2 + x + b = 0

Condition for roots,

For equal and real roots, b2 – 4ac = 0

For unequal and real roots, b2 – 4ac > 0

For imaginary roots, b2 – 4ac < 0

Calculation:

For equal and real roots, b2 – 4ac = 0

⇒ b² = 4ac

After comparing with the general form of the quadratic equation we'll get

b = 1, a = a and c = b

Then, b2 = 4ac

⇒ 1 = 4ab

⇒ ab = 1/4

∴ The correct relation is ab = 1/4

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