Question

If $\alpha$ and $\beta$ are the roots of the equation $a{x}^2+bx+c=0$, then the value of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$ is $\frac{b^2-2ac}{ac}$. State true or false.

• A. True
• B. False

Answer 1

The correct option is A True

The equation is $a{x}^2+bx+c=0$
The value of $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }$
= $\frac{{\alpha }^2+{\beta }^2}{\alpha \beta }$
= $\frac{(\alpha +\beta {)}^2-2\alpha \beta }{\alpha \beta }$
= $\frac{(\frac{-b}{a}{)}^2-2\frac{c}{a}}{\frac{c}{a}}$
= $\frac{b^2-2ac}{ac}$