Question

The quadratic equation $x^2+bx+c=0$ has real roots $\alpha and\beta$. If a, b, c real and of the same sign then

• A. $\alpha and\beta$ are both positive
• B. $\alpha and\beta$ are both negative
• C. $\alpha and\beta$ are of opposite sign
• D. Nothing can be said about the signs of $\alpha and\beta$ as the information is insufficient

Answer 1

Answer: (B)

$\alpha and\beta$ are both negative

The quadratic equation $x^2+bx+c=0$
Then $a=1,b=b$ and $c=c$
Sum of roots $=\alpha +\beta$=$\frac{-b}{1}=b$
Or product of roots $=\alpha \beta =\frac{c}{1}=c$
Then $\alpha$$\beta$ both are negative