If $α, β$ are roots of the equation $x^{2} - 5 x + 6 = 0$ , then the equation whose roots are $(α + 3)$ and $(β + 3)$ is

2 x^{2} - 11 x + 30 = 0

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- x^{2} + 11 x = 0

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x^{2} - 11 x + 30 = 0

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2 x^{2} - 22 x + 60 = 0

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Solution

The correct options are
B $x^{2} - 11 x + 30 = 0$
D $2 x^{2} - 22 x + 60 = 0$
Given quadratic equation is $x^{2} - 5 x + 6 = 0$
Let $α + 3 = x$
$∴ α = x - 3$ (replace x by x-3)
So the required equation is
$(x - 3)^{2} - 5 (x - 3) + 6 = 0$
$\Rightarrow x^{2} - 6 x + 9 - 5 x + 15 + 6 = 0$
$\Rightarrow x^{2} - 11 x + 30 = 0$
$\Rightarrow (x^{2} - 11 x + 30) \times 2 = 0$
$\Rightarrow 2 x^{2} - 22 x + 60 = 0$

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