If $p$ and $q$ are the roots of the equation $a x^{2} + b x + c = 0$ , then the value of $\frac{p}{q} + \frac{q}{p}$ is

b^{2} - 2 a c

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\frac{b^{2} - 2 a c}{a c}

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\frac{b^{2} - 4 a c}{2 a}

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\frac{b^{2} - 4 a c}{a c}

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Solution

The correct option is A $\frac{b^{2} - 2 a c}{a c}$
and q are the roots of $a x^{2} + b x + c = 0$ .Then
$p + q = - \frac{b}{a}, p q = \frac{c}{a}$
$\frac{p}{q} + \frac{q}{p} = \frac{p^{2} + q^{2}}{p q} = \frac{(p + q)^{2} - 2 p q}{p q}$
$= \frac{(b^{2} - a^{2}) - 2 (c / a)}{c / a} = \frac{b^{2} - 2 a c}{a^{2}} \times \frac{a}{c} = \frac{b^{2} - 2 a c}{a c}$

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Similar questions

If b² – 4ac = 0 then The roots of the Quadratic equation ax² + bx + c = 0 are given by :

Q. What are the roots of the quadratic equation

a x^{2} + b x + c = 0 ?

Q. Which of the given formulae is the correct one to find out the roots of the quadratic equation

a x^{2} + b x + c = 0

The roots of a quadratic equation $a x^{2} + b x + c = 0$ are given by $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , provided $b^{2} - 4 a c \geq 0$ .

Q. For the equation

a x^{2} + b x + c = 0

which of the following statements is incorrect?
(a) If (b² − 4ac) < 0, the roots are imaginary.
(b) If (b² − 4ac) = 0, the roots are real and equal.
(c) If (b² − 4ac) > 0 and (b² − 4ac) is a perfect square, then the roots are rational and unequal.
(d) (b² − 4ac) < 0, the roots are irrational.

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If p and q are the roots of the equation ax2+bx+c=0, then the value of pq+qp is

The correct option is A b2−2acacand q are the roots of ax2+bx+c=0.Thenp+q=−ba,pq=capq+qp=p2+q2pq=(p+q)2−2pqpq=(b2−a2)−2(c/a)c/a=b2−2aca2×ac=b2−2acac

If $p$ and $q$ are the roots of the equation $a x^{2} + b x + c = 0$ , then the value of $\frac{p}{q} + \frac{q}{p}$ is