Let $α, β$ be the values of m for which the equation $(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m)$ has equal roots. Find the equation whose roots are $α + 2$ and $β + 2$ .

$x^{2} - 4 x + 3 = 0$

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$x^{2} - 5 x + 6 = 0$

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$x^{2} - 3 x = 0$

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$x^{2} - 7 x + 10 = 0$

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Solution

The correct option is D
$x^{2} - 7 x + 10 = 0$

$△ = 0 \Rightarrow (2 (1 + 3 m))^{2} - 4 (1 + m) (1 + 8 m) = 0$
$\Rightarrow 1 + 9 m^{2} + 6 m - 1 - 9 m - 8 m^{2} = 0$
$\Rightarrow m^{2} - 3 m = 0$
$\Rightarrow m (m - 3) = 0$
$\Rightarrow α = 0, β = 3$
$\Rightarrow α + 2 = 2$ and $β + 2 = 5$
Equation whose roots are $α + 2$ and $β + 2$ is $(x - 2) (x - 5) = x^{2} - 7 x + 10 = 0$

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Let $α, β$ be the values of m for which the equation $(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m)$ has equal roots. Find the equation whose roots are $α + 2$ and $β + 2$ .

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Let α,β be the values of m for which the equation (1+m)x2−2(1+3m)x+(1+8m) has equal roots. Find the equation whose roots are α+2 and β+2.

The correct option is D x2−7x+10=0 △=0⇒(2(1+3m))2−4(1+m)(1+8m)=0 ⇒1+9m2+6m−1−9m−8m2=0 ⇒m2−3m=0 ⇒m(m−3)=0 ⇒α=0 ,β=3 ⇒α+2=2 and β+2=5 Equation whose roots are α+2 and β+2 is (x−2)(x−5)=x2−7x+10=0

Let $α, β$ be the values of m for which the equation $(1 + m) x^{2} - 2 (1 + 3 m) x + (1 + 8 m)$ has equal roots. Find the equation whose roots are $α + 2$ and $β + 2$ .