If the roots of the equation ax^2 + bx + c = | vedclass

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

Question

(B) Given the quadratic equation $ax^2 + bx + c = 0$ with roots $l$ and $2l$.Sum of roots: $l + 2l = -\frac{b}{a}$ $\Rightarrow 3l = -\frac{b}{a}$ $\R

Vedclass · Accepted Answer

$2b^2 = 9ac$

Vedclass · Answer

(B) Given the quadratic equation $ax^2 + bx + c = 0$ with roots $l$ and $2l$.Sum of roots: $l + 2l = -\frac{b}{a}$ $\Rightarrow 3l = -\frac{b}{a}$ $\Rightarrow l = -\frac{b}{3a}$ $(i)$Product of roots: $l 	imes 2l = \frac{c}{a} \Rightarrow 2l^2 = \frac{c}{a}$ $(ii)$Substituting $(i)$ into $(ii)$:$2\left(-\frac{b}{3a}ight)^2 = \frac{c}{a}$$2\left(\frac{b^2}{9a^2}ight) = \frac{c}{a}$$\frac{2b^2}{9a^2} = \frac{c}{a}$$2b^2 = 9ac$Alternatively,for a quadratic equation $ax^2 + bx + c = 0$ with roots in ratio $m:n$,the condition is $mnb^2 = (m+n)^2ac$. Here $m=1, n=2$,so $1 	imes 2 	imes b^2 = (1+2)^2ac \Rightarrow 2b^2 = 9ac$.

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

Similar Questions

If $\alpha, \beta$ and $\gamma$ are the roots of ${x^3} + px + q = 0$,then the value of ${\alpha^3} + {\beta^3} + {\gamma^3}$ is equal to

Let $\alpha, \beta$ be roots of $x^2+\sqrt{2}x-8=0$. If $U_n = \alpha^n + \beta^n$,then $\frac{U_{10} + \sqrt{2}U_9}{2U_8}$ is equal to ............

If $\tan A$ and $\tan B$ are the roots of the equation $5x^2 - 4x + 1 = 0$, then the value of $A + B$ is...

If $\alpha, \beta, \gamma$ are roots of the equation $x^3 + qx - r = 0$,then find the equation whose roots are $\left( \beta \gamma + \frac{1}{\alpha} \right), \left( \gamma \alpha + \frac{1}{\beta} \right), \left( \alpha \beta + \frac{1}{\gamma} \right)$.

If the harmonic mean between the roots of $(5+\sqrt{2}) x^2-b x+(8+2 \sqrt{5})=0$ is $4$,then the value of $b$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module