First slide

Theory of equations

Question

If the ratio of the roots of the equation ${ax}^{2} + bx + c = 0$ be $p : q,$ then

Moderate

A

${pqb}^{2} + {(p + q)}^{2} ac = 0$
B

${pqb}^{2} - {(p + q)}^{2} ac = 0$
C

${pqa}^{2} - {(p + q)}^{2} bc = 0$
D

None of these

Solution

Let $pα, qα$ be the roots of the given equation ${ax}^{2} + bx + c = 0$
Then $pα + qα = - \frac{b}{a} and pα . qα = \frac{c}{a}$
From first relation, $α = - \frac{b}{a (p + q)}$
Substituting this value of $α$ in second relation, we get
$\frac{b^{2}}{a^{2} {(p + q)}^{2}} \times pq = \frac{c}{a} \Rightarrow b^{2} pq - ac {(p + q)}^{2} = 0$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App