If - - are the roots of x2-7 x-5-0- then the equation whose roots are -1- -1 is A- x2-5 x-1-0B- x2-7 x-13-0- x2-5 x-1-0D- x2-9 x-13-0

The correct option is D x^2+9x+13=0f(x) = x^2+7x+5 = 0 →roots are α, β The equation whose roots are α 1, β 1 is, f(x+1)= 0 ⇒ (x+1)^2+7(x+1)+5 = 0 ⇒ x^2+2x+1 ...

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Standard XII

Mathematics

Relation between Roots and Coefficients for Quadratic

If α, β are t...

Question

If $α, β$ are the roots of $x^{2} + 7 x + 5 = 0$ , then the equation whose roots are $α - 1, β - 1$ is

x^{2} + 5 x - 1 = 0

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x^{2} + 7 x + 13 = 0

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x^{2} + 9 x + 13 = 0

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x^{2} + 5 x + 1 = 0

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Solution

The correct option is C $x^{2} + 9 x + 13 = 0$
$f (x) = x^{2} + 7 x + 5 = 0 \to roots are α, β$
The equation whose roots are $α - 1, β - 1$ is,
$f (x + 1) = 0$
$\Rightarrow (x + 1)^{2} + 7 (x + 1) + 5 = 0 \Rightarrow x^{2} + 2 x + 1 + 7 x + 7 + 5 = 0 \Rightarrow x^{2} + 9 x + 13 = 0$

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Similar questions

Q. If

α & β

are roots if the equation

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

, then evaluate

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Q. If

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, then the equation whose roots are

α - 1, β - 1

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If α,β are the roots of x2+7x+5=0, then the equation whose roots are α−1,β−1 is

The correct option is C x2+9x+13=0f(x)=x2+7x+5=0→roots are α,β The equation whose roots are α−1,β−1 is, f(x+1)=0 ⇒(x+1)2+7(x+1)+5=0⇒x2+2x+1+7x+7+5=0⇒x2+9x+13=0

If $α, β$ are the roots of $x^{2} + 7 x + 5 = 0$ , then the equation whose roots are $α - 1, β - 1$ is

The correct option is C $x^{2} + 9 x + 13 = 0$
$f (x) = x^{2} + 7 x + 5 = 0 \to roots are α, β$
The equation whose roots are $α - 1, β - 1$ is,
$f (x + 1) = 0$
$\Rightarrow (x + 1)^{2} + 7 (x + 1) + 5 = 0 \Rightarrow x^{2} + 2 x + 1 + 7 x + 7 + 5 = 0 \Rightarrow x^{2} + 9 x + 13 = 0$