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Question: If the roots of the equation ax<sup>2</sup>+ bx + c = 0, are the form \(\frac{\alpha}{\alpha - 1}\) ...

If the roots of the equation ax2+ bx + c = 0, are the form αα−1\frac{\alpha}{\alpha - 1} and α+1α\frac{\alpha + 1}{\alpha}then the value of (a + b + c)2 is –

A

2b2 – ac

B

b2 – 2ac

C

b2 – 4ac

D

4b2 – 2ac

Answer

b2 – 4ac

Explanation

Solution

αα−1+α+1α=−ba\frac{\alpha}{\alpha - 1} + \frac{\alpha + 1}{\alpha} = - \frac{b}{a} and αα−1⋅α+1α=ca\frac{\alpha}{\alpha - 1} \cdot \frac{\alpha + 1}{\alpha} = \frac{c}{a}

2α2−1α2−α\frac{2\alpha^{2} - 1}{\alpha^{2} - \alpha} = – ba\frac{b}{a} and a = c+ac−a\frac{c + a}{c - a}

(c + a)2 + 4ac = – 2b (c + a)

Ž (c + a)2 + 2b(c + a) + b2 = b2 – 4ac

Ž (a + b + c)2 = b2 – 4ac