If the ratio of the roots of the equation ax^ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the roots of the equation $ax^2 + bx + c = 0$ be $p\alpha$ and $q\alpha$.From the relationship between roots and coefficients:$p\alpha + q\alp

Vedclass · Accepted Answer

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

Vedclass · Answer

(B) Let the roots of the equation $ax^2 + bx + c = 0$ be $p\alpha$ and $q\alpha$.From the relationship between roots and coefficients:$p\alpha + q\alpha = -\frac{b}{a} \implies \alpha(p + q) = -\frac{b}{a} \implies \alpha = -\frac{b}{a(p + q)}$Also,$p\alpha \cdot q\alpha = \frac{c}{a} \implies pq\alpha^2 = \frac{c}{a}$Substituting the value of $\alpha$ in the second equation:$pq \left( -\frac{b}{a(p + q)} \right)^2 = \frac{c}{a}$$pq \cdot \frac{b^2}{a^2(p + q)^2} = \frac{c}{a}$Multiplying both sides by $a^2(p + q)^2$:$pqb^2 = ac(p + q)^2$$pqb^2 - (p + q)^2ac = 0$

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

Similar Questions

Let $\alpha$ and $\beta$ be two distinct roots of the equation $x^3 + 3x^2 - 1 = 0$. The equation which has $(\alpha \beta)$ as its root is equal to

The expression $x^3 - 3x^2 - 9x + c$ can be written in the form $(x - a)^2 (x - b)$ if the value of $c$ is

If $A.M.$ and $G.M.$ of roots of a quadratic equation are $8$ and $5,$ respectively,then obtain the quadratic equation.

The cubic equation whose roots are the squares of the roots of the equation $x^3-2x^2+3x-4=0$ is

If $\tan \theta$ and $\cot \theta$ are two distinct roots of the equation $ax^2 + bx + c = 0$,$a \neq 0, b \neq 0$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module