If the two equations x^2 - cx + d = 0 and x^2 - ax + b = 0 have o… - Vidyadip

MCQ

If the two equations ${x^2} - cx + d = 0$ and ${x^2} - ax + b = 0$ have one common root and the second has equal roots, then $2(b + d) = $

A
$0$
B
$a + c$
✓
$ac$
D
$ - ac$

✓

Answer

Correct option: C.

$ac$

c
(c) Let roots of ${x^2} - cx + d = 0$be $\alpha ,\beta $ then roots of ${x^2} - ax + b = 0$ be $\alpha ,\alpha $

$\alpha + \beta = c,\alpha \beta = d,\alpha + \alpha = a,{\alpha ^2} = b$

Hence $2(b + d) = 2({\alpha ^2} + \alpha \beta ) = 2\alpha (\alpha + \beta ) = ac$

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