Question

If the zeroes of a quadratic polynomial $a{x}^2+bx+c$ are both negative, then which of the following is always correct

• A. $\frac{-b}{a}>0$
• B. $\frac{c}{a}=0$
• C. $a,b$ and $c$ all are zero
• D. $a,b$ and $c$ all have same sign

Answer 1

The correct option is D $a,b$ and $c$ all have same sign

Given the zeroes of the quadratic polynomial $a{x}^2+bx+c$ are both negative.

Then the sum of the zeroes be also negative, then

$-\frac{b}{a}<0$

or, $\frac{b}{a}>0$.......(1).

And the product of the zeroes is positive then,

$\frac{c}{a}>0$.......(2).

$F\left(0\right)=c>0\Rightarrow a>0\Rightarrow b>0$

From (1) and (2) it follows that $a,b,c$ all have the same sign.