If - - are the roots of ax2-bx-c-0 and - -k- - -k are the roots of px2-qx-r-0- then b2-4ac-q2-4pr is equal to-

The correct option is C (a/p)^2 Absolute difference of both the roots will be same, ⇒|√(D_1)a|=|√(D_2)p| Where D_1,D_2 are the discriminant of t ...

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Standard X

Mathematics

Discriminant

If α, β are...

Question

If $α, β$ are the roots of $a x^{2} + b x + c = 0$ and $α + k, β + k$ are the roots of $p x^{2} + q x + r = 0$ , then $\frac{b^{2} - 4 a c}{q^{2} - 4 p r}$ is equal to:

\frac{a}{p}

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{(\frac{a}{p})}^{2}

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Solution

The correct option is C ${(\frac{a}{p})}^{2}$
Absolute difference of both the roots will be same,
$\Rightarrow ∣ ∣ ∣ \frac{\sqrt{D_{1}}}{a} ∣ ∣ ∣ = ∣ ∣ ∣ \frac{\sqrt{D_{2}}}{p} ∣ ∣ ∣$
Where $D_{1}, D_{2}$ are the discriminant of the respective quadratic
$\Rightarrow \frac{D_{1}}{D_{2}} = \frac{a^{2}}{p^{2}}$ , square above equation
$\Rightarrow \frac{b^{2} - 4 a c}{q^{2} - 4 p r} = {(\frac{a}{p})}^{2}$

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If α,β are the roots of ax2+bx+c=0 and α+k,β+k are the roots of px2+qx+r=0, then b2−4acq2−4pr is equal to:

The correct option is C (ap)2Absolute difference of both the roots will be same,⇒∣∣∣√D1a∣∣∣=∣∣∣√D2p∣∣∣Where D1,D2 are the discriminant of the respective quadratic⇒D1D2=a2p2, square above equation ⇒b2−4acq2−4pr=(ap)2

If $α, β$ are the roots of $a x^{2} + b x + c = 0$ and $α + k, β + k$ are the roots of $p x^{2} + q x + r = 0$ , then $\frac{b^{2} - 4 a c}{q^{2} - 4 p r}$ is equal to: