Question

If p is not equal to q and p^2=5p-3 and q^2=5q-3 the equation having roots as p/q and q/p is

Answer 1

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Answer 2

Answer:

The required equation is $pqx^2-(5p+5q-6)x+pq=0$.

Step-by-step explanation:

It is given that

$p^2=5p-3$

$q^2=5q-3$

If α and β are two roots of the equation $ax^2+bx+c=0$, then

$\alpha +\beta =-\frac{b}{a}$

$\alpha \times \beta =\frac{c}{a}$

If p/q and q/p are roots of the equation then

$\frac{p}{q} +\frac{q}{p}=\frac{p^2+q^2}{pq}$

$\frac{p}{q} +\frac{q}{p}=\frac{5p-3+5q-3}{pq}$

$\frac{p}{q} +\frac{q}{p}=\frac{5p+5q-6}{pq}$

$-\frac{b}{a}=\frac{5p+5q-6}{pq}$

The product of roots are

$\frac{p}{q}\times \frac{q}{p}=1$

$\frac{c}{a}=1$

$c=a=pq$.

Therefore the required equation is

$pqx^2-(5p+5q-6)x+pq=0$