Question

If α and β are the roots of the equation ax² + bx + c = 0 and if px² + qx + r = 0 has roots \(\frac{1-α}{α}\) and \(\frac{1-β}{β}\), then r equals :

(a) abc 

(b) a + 2b 

(c) a + b + c 

(d) ab + bc + ca.

Answer 1

(c) a + b + c.

As α, β are the roots of the equation ax² + bx + c = 0, so

α + β = \(-\frac{b}{a}\), αβ = \(\frac{c}{a}\)

The equation whose roots are \(\frac{1-α}{α}\) and \(\frac{1-β}{β}\) can be written as :

⇒ cx² + (b + 2c)x + (a + b + c) = 0                ...(i) 

Compairing eqn. (i) with the given equation px² + qx + r = 0, 

we get r = a + b + c.