The condition that one root of the equation a | vedclass

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

Question

(C) Let the roots of the equation $ax^2 + bx + c = 0$ be $\alpha$ and $3\alpha$.From the relationship between roots and coefficients:Sum of roots: $\a

Vedclass · Accepted Answer

$3b^2 = 16ac$

Vedclass · Answer

(C) Let the roots of the equation $ax^2 + bx + c = 0$ be $\alpha$ and $3\alpha$.From the relationship between roots and coefficients:Sum of roots: $\alpha + 3\alpha = -\frac{b}{a}$ $\Rightarrow 4\alpha = -\frac{b}{a}$ $\Rightarrow \alpha = -\frac{b}{4a}$.Product of roots: $\alpha \cdot 3\alpha = \frac{c}{a} \Rightarrow 3\alpha^2 = \frac{c}{a}$.Substituting the value of $\alpha$ in the product equation:$3\left(-\frac{b}{4a}\right)^2 = \frac{c}{a}$$3 \cdot \frac{b^2}{16a^2} = \frac{c}{a}$$3b^2 = 16ac$.

The condition that one root of the equation $ax^2 + bx + c = 0$ is three times the other is:

Similar Questions

If the sum of the roots of the equation $x^2 + px + q = 0$ is three times their difference,then which one of the following is true?

If one root of the equation $ax^2 + bx + c = 0$ is the square of the other root,then $b^3 + a^2c + ac^2 = \dots$

If $p$ and $q$ are the roots of the equation $x^2 + pq = (p + 1)x$,then $q=$

If one root of the equation $x^2 - 30x + p = 0$ is the square of the other root,then $p = \dots \dots \dots$

If $\alpha, \beta, \gamma$ are the roots of $x^3+ax^2+bx+c=0$,then find the value of $\sum \frac{1}{\alpha}$,given that $\alpha, \beta, \gamma$ are non-zero.

Vedclass Test Series

Exam Paper Generator

Online Exam Module