Find p 1-2 q 2- p 3 q 3- p 8 q 3 if p and q are the roots of the equation mx 2-2 n x - v -0A- m n v-n2-v2 m-4-B- v2v-2 n-m3C- v2-m3D- n v2-m3

The correct option is B Assume the roots p and q = 1 and 2 respectively. Sum of roots = ( 2n/m)=3 Product of roots =v/m=2 Write all the terms is the form o ...

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Find p 1/2 q ...

Question

Find $p^{\frac{1}{2}} q^{2} + p^{3} q^{3} + p^{8} q^{3}$ if p and q are the roots of the equation $m x^{2} - 2 n x + v = 0$

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Solution

The correct option is B

Assume the roots p and q = 1 and 2 respectively.

Sum of roots $= - (- \frac{2 n}{m}) = 3$

Product of roots $= \frac{v}{m} = 2$

Write all the terms is the form of variable m,

$\frac{2 n}{m} = 3 \Rightarrow n = \frac{3 m}{2}$

$\frac{v}{m} = 2 \Rightarrow v = 2 m$

$p^{\frac{1}{2}} q^{2} + p^{3} q^{3} + p^{8} q^{3} = 20$

Substitute values in terms of m in answer options. Only option b gives 20

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Find p12q2+p3q3+p8q3 if p and q are the roots of the equation mx2−2nx+v=0

The correct option is B Assume the roots p and q = 1 and 2 respectively. Sum of roots =−(−2nm)=3 Product of roots =vm=2 Write all the terms is the form of variable m, 2nm=3⇒n=3m2 vm=2⇒v=2m p12q2+p3q3+p8q3=20 Substitute values in terms of m in answer options. Only option b gives 20

Find $p^{\frac{1}{2}} q^{2} + p^{3} q^{3} + p^{8} q^{3}$ if p and q are the roots of the equation $m x^{2} - 2 n x + v = 0$