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Question

If x=p+2q+p2qp+2qp2q, show that qx2px+q=0

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Solution

x=p+2q+p2qp+2qp2q

x=p+2q+p2qp+2qp2q×p+2q+p2qp+2q+p2q

x=p+2q+p2q+2p24q2p+2qp+2q

x=p+p24q22q

Comparing with root b+b24ac2a of equation ax2+bx+c=0 which satisfy this quadratic equation.

For calculated x, b=p,a=q,c=c=q

Hence given value of x satisfy equation

qx2px+q=0



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