If p- q are roots of an equation x2-5 x-2-0- then find out the value of p-q-q-p-A- 15-2B- 25-2C- 21-2D- 17

The correct option is C Sum of the roots:p+q= 5 Product of the roots:pq=2 p/q+q/p=(p^2+q^2)/pq=[(p+q)^2 2pq]/pq =[(p+q)^2]/pq 2=25/2 2=21/2 ...

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Quantitative Aptitude

Quadratic Equations

If p, q are r...

Question

If p, q are roots of an equation $x^{2} + 5 x + 2 = 0$ , then find out the value of $\frac{p}{q} + \frac{q}{p} .$

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Solution

The correct option is C
Sum of the roots: $p + q = - 5$

Product of the roots: $p q = 2$

$\frac{p}{q} + \frac{q}{p} = \frac{(p^{2} + q^{2})}{p q} = \frac{[(p + q)^{2} - 2 p q]}{p q} = \frac{[(p + q)^{2}]}{p q} - 2 = \frac{25}{2} - 2 = \frac{21}{2}$

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If p, q are roots of an equation x2+5x+2=0 , then find out the value of pq+qp.

The correct option is C Sum of the roots: p+q=−5 Product of the roots: pq=2 pq+qp=(p2+q2)pq=[(p+q)2−2pq]pq=[(p+q)2]pq−2=252−2=212

If p, q are roots of an equation $x^{2} + 5 x + 2 = 0$ , then find out the value of $\frac{p}{q} + \frac{q}{p} .$

The correct option is C
Sum of the roots: $p + q = - 5$

Product of the roots: $p q = 2$

$\frac{p}{q} + \frac{q}{p} = \frac{(p^{2} + q^{2})}{p q} = \frac{[(p + q)^{2} - 2 p q]}{p q} = \frac{[(p + q)^{2}]}{p q} - 2 = \frac{25}{2} - 2 = \frac{21}{2}$