If r is the ratio of the roots of the equation x2-5x-8-0- then r-12r is equal to

X^2 5x+8=0 Let the roots be α, β Sum and product of the roots is, α+ β=5, αβ=8 nbsp; Let r = αβ Now, (r+1)^2r =(α/β+1)^2α/β =(α+β)^2αβ =258 ...

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Standard XIII

Mathematics

Algebra of Roots of Quadratic Equations

If r is the r...

Question

If $r$ is the ratio of the roots of the equation $x^{2} - 5 x + 8 = 0$ , then $\frac{(r + 1)^{2}}{r}$ is equal to

\frac{9}{8}

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\frac{64}{5}

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- \frac{1}{40}

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\frac{25}{8}

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Solution

The correct option is D $\frac{25}{8}$
$x^{2} - 5 x + 8 = 0$
Let the roots be $α, β$
Sum and product of the roots is,
$α + β = 5, α β = 8$
Let $r = \frac{α}{β}$
Now, $\frac{(r + 1)^{2}}{r}$
$= \frac{(\frac{α}{β} + 1)^{2}}{\frac{α}{β}} = \frac{(α + β)^{2}}{α β} = \frac{25}{8}$

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Algebra of Roots of Quadratic Equations

Standard XIII Mathematics

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If r is the ratio of the roots of the equation x2−5x+8=0, then (r+1)2r is equal to

The correct option is D 258 x2−5x+8=0 Let the roots be α,β Sum and product of the roots is, α+β=5, αβ=8 Let r=αβ Now, (r+1)2r =(αβ+1)2αβ=(α+β)2αβ=258

If $r$ is the ratio of the roots of the equation $x^{2} - 5 x + 8 = 0$ , then $\frac{(r + 1)^{2}}{r}$ is equal to

The correct option is D $\frac{25}{8}$
$x^{2} - 5 x + 8 = 0$
Let the roots be $α, β$
Sum and product of the roots is,
$α + β = 5, α β = 8$
Let $r = \frac{α}{β}$
Now, $\frac{(r + 1)^{2}}{r}$
$= \frac{(\frac{α}{β} + 1)^{2}}{\frac{α}{β}} = \frac{(α + β)^{2}}{α β} = \frac{25}{8}$