Question

If the sum of two roots of the equation $x^3+a{x}^2+bx+c=0$ is zero, then value of $ab$ equals

• A. $c$
• B. $2c$
• C. $-2c$
• D. $-c$

Answer 1

The correct option is A $c$

Given equation is $x^3+a{x}^2+bx+c=0$

Let the roots be $\alpha ,-\alpha ,\beta$

Then $\alpha -\alpha +\beta =-a$

$\Rightarrow \beta =-a$ ....(1)

Also, $-{\alpha }^2+\alpha \beta -\alpha \beta =b$

$\Rightarrow -{\alpha }^2=b$ .....(2)

Also, $-{\alpha }^2\beta =-c$ ....(by (1)and (2))

$\Rightarrow -ab=-c$

$\Rightarrow ab=c$