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Question: If a, b are the roots of the equation ax<sup>2</sup> + bx + c = 0, then the roots of the equation ax...

If a, b are the roots of the equation ax2 + bx + c = 0, then the roots of the equation ax2 + bx(x + 1) + c(x + 1)2 = 0 are :

A

a –1, b –1

B

a + 1, b + 1

C

αα–1\frac{\alpha}{\alpha –1}, ββ–1\frac{\beta}{\beta –1}

D

α1–α\frac{\alpha}{1–\alpha}, β1–β\frac{\beta}{1–\beta}

Answer

α1–α\frac{\alpha}{1–\alpha}, β1–β\frac{\beta}{1–\beta}

Explanation

Solution

a(xx+1)2\left( \frac{x}{x + 1} \right)^{2} + b (xx+1)\left( \frac{x}{x + 1} \right) + c = 0

xx+1\frac{x}{x + 1} = a

x = ax + a

x = α1–α\frac{\alpha}{1–\alpha}