If - - are the roots of the equation x 2-4 x -1-0- then the equation whose roots are 3 -5-3 -5 is A- 9 x 2-18 x -4-0B- x2-22 x-76-0- x2-22 x-76-0D- x2-2 x-44-0

The correct option is C x^2+22x+76=0f(x) =x^2 +4x 1 f(x)=0 →α, β nbsp;are the roots. Equation whose roots are 3α 5,3β 5 is f(x+53)= 0 ⇒(x+53)^2 +4(x+53) 1 ...

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Byju's Answer

Standard XIII

Mathematics

Relation between Roots and Coefficients for Quadratic

If α, β are t...

Question

If $α, β$ are the roots of the equation $x^{2} + 4 x - 1 = 0$ , then the equation whose roots are $3 α - 5, 3 β - 5$ is

9 x^{2} - 18 x + 4 = 0

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x^{2} + 22 x - 76 = 0

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x^{2} + 22 x + 76 = 0

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x^{2} + 2 x - 44 = 0

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Solution

The correct option is C $x^{2} + 22 x + 76 = 0$
$f (x) = x^{2} + 4 x - 1$
$f (x) = 0 \to α, β$ are the roots.
Equation whose roots are $3 α - 5, 3 β - 5$ is
$f (\frac{x + 5}{3}) = 0$
$\Rightarrow {(\frac{x + 5}{3})}^{2} + 4 (\frac{x + 5}{3}) - 1 = 0 \Rightarrow x^{2} + 22 x + 76 = 0$

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If α,β are the roots of the equation x2+4x−1=0, then the equation whose roots are 3α−5,3β−5 is

The correct option is C x2+22x+76=0f(x)=x2+4x−1 f(x)=0→α,β are the roots. Equation whose roots are 3α−5,3β−5 is f(x+53)=0 ⇒(x+53)2+4(x+53)−1=0⇒x2+22x+76=0

If $α, β$ are the roots of the equation $x^{2} + 4 x - 1 = 0$ , then the equation whose roots are $3 α - 5, 3 β - 5$ is

The correct option is C $x^{2} + 22 x + 76 = 0$
$f (x) = x^{2} + 4 x - 1$
$f (x) = 0 \to α, β$ are the roots.
Equation whose roots are $3 α - 5, 3 β - 5$ is
$f (\frac{x + 5}{3}) = 0$
$\Rightarrow {(\frac{x + 5}{3})}^{2} + 4 (\frac{x + 5}{3}) - 1 = 0 \Rightarrow x^{2} + 22 x + 76 = 0$