Question

If the roots of the equation $a{x}^2+bx+c=0$ are $\alpha$ and $\beta$, then the quadratic equation whose roots are $-\alpha$ and $-\beta$ is

• A. $a{x}^2-bx-c=0$
• B. $a{x}^2-bx+c=0$
• C. $a{x}^2-bx-c=0$
• D. $a{x}^2-bx+2c=0$

Answer 1

Answer: (B)

$a{x}^2-bx+c=0$

For

$2x^2+bx+c=0$, roots are $\alpha$ and $\beta$

$\alpha +\beta =-\frac{b}{a}$

$\alpha \beta =\frac{c}{a}$

For another quadratic equation, roots are $-\alpha -\beta$

Sum of roots

$=-\alpha -\beta$

$=-(\alpha +\beta )$

$=-(-\frac{b}{a})$

$=\frac{b}{a}$

Product of roots

$=(-\alpha )(-\beta )$

$=-\left(\alpha \beta \right)$

$=\frac{c}{a}$

So, equation is $a{x}^2-bx+c=0$

option $B$ is correct.