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

0

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a + c

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a c

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- a c

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Solution

The correct option is C $a c$
Given quadratic equations
$x^{2} - c x + d = 0$ ....(1)
Let $α, β$ be the roots of equation (1)
$x^{2} - a x + b = 0$ .....(2)
Let $α, α$ be the roots of equation (2)
$2 α = a$
$α = \frac{a}{2}$
Also , $α^{2} = b$
Since, $α$ is a root of (1),
$α^{2} - c α + d = 0$
$b + d = \frac{a c}{2}$
$\Rightarrow 2 (b + d) = a c$

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Similar questions

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

x^{2} - c x + d = 0, x^{2} - a x + b = 0

2 (b + d) =

c^{2} = 4 d

x^{2} - a x + b

x^{2} - c x + d = 0

2 (b + d)

x^{2} + a x + b = 0

x^{2} + c x + d = 0

x^{2} + x (2 a - c) + (a^{2} - a c + d) = 0

x^{2} + a x + b c = 0,

x^{2} + b x + a c = 0,

a \neq b

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