Question

The quadratic equation abx2 + acx + b(bx + c) = 0 has non-zero equal and rational roots. The values of a and c respectively cannot be equal to (ab ď‚ą 0)

Answer 1

Thank you for asking this question here is your answer:

quadratic equation is abx² + acx + b(bx + c) = 0

or, abx² + acx + b²x + bc = 0

A/C to question,

roots are equal and rational numbers .

so, discriminant = 0

(ac + b²)² - 4(ab)(bc) = 0

a²c² + b⁴ + 2ab²c - 4ab²c = 0

a²c² + b⁴ - 2ab²c = 0

(ac)² + (b²)² - 2(ac)(b²) = 0

(ac - b²)² = 0

so, ac = b²

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