Question

The equation whose roots are the squares of the roots of the equation ax² + bx + c = 0 is

• A. a²x² + b²x + c² = 0
• B. a²x² – (b² –4ac)x +c² =0
• C. a²x² – (b² –2ac)x +c² =0
• D. a²x² + (b² –ac)x +c² =0

Answer 1

Answer: (C)

a²x² – (b² –2ac)x +c² =0

Answer 2

Given eqⁿ ax² + bx + c = 0

Let its roots are α, β

then α + β = –b/a

αβ = c/a

For reqd. eqⁿ roots are α², β²

then α² + β² = (α + β)² – 2αβ = $\frac{b^{2} - 2ca}{a^{2}}$

and α²β² = c²/a²

So reqd. eqⁿ = a²x² – (b² – 2ca) x + c² = 0