If alpha and beta are the roots of the equati | vedclass

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

Question

(D) For the quadratic equation $x^{2}+3ax+2a^{2}=0$,the sum of the roots $\alpha+\beta = -\frac{b}{a_{coeff}} = -3a$ and the product of the roots $\al

Vedclass · Accepted Answer

$\pm 1$

Vedclass · Answer

(D) For the quadratic equation $x^{2}+3ax+2a^{2}=0$,the sum of the roots $\alpha+\beta = -\frac{b}{a_{coeff}} = -3a$ and the product of the roots $\alpha\beta = \frac{c}{a_{coeff}} = 2a^{2}$.We know that $\alpha^{2}+\beta^{2} = (\alpha+\beta)^{2} - 2\alpha\beta$.Given $\alpha^{2}+\beta^{2} = 5$,we substitute the values:$5 = (-3a)^{2} - 2(2a^{2})$$5 = 9a^{2} - 4a^{2}$$5 = 5a^{2}$$a^{2} = 1$$a = \pm 1$.

If $\alpha$ and $\beta$ are the roots of the equation $x^{2}+3ax+2a^{2}=0$ and if $\alpha^{2}+\beta^{2}=5$,find the value of $a$.

Similar Questions

The roots of $\frac{x+4}{x-4}+\frac{x-4}{x+4}=\frac{10}{3}$ are:

Solve the given two equations and select the correct answer from the given options.
$I.$ $2x^2 - 3x - 35 = 0$
$II.$ $y^2 - 7y + 6 = 0$

The expression $x^2-x+1$ has:

Solve the given two equations and select the correct answer from the given options.
$I.$ $\frac{12 \times 4}{x^{4/7}} - \frac{3 \times 4}{x^{4/7}} = x^{10/7}$
$II.$ $y^3 + 783 = 999$

Solve the given two equations and select the correct answer from the given options.
$I.$ $x = \sqrt[3]{4913}$
$II.$ $13y + 3x = 246$

Vedclass Test Series

Exam Paper Generator

Online Exam Module