Question

# If one of the zeroes of a quadratic polynomial of the form ${{x}^{2}}+ax+b$ is the negative of the other, then it (a) has no linear term and the constant term is negative. (b) has no linear term and the constant term is positive. (c) can have a linear term but the constant term is negative. (d) can have a linear term but the constant term is positive.

Hint: Write the quadratic equation in terms of roots. So by this we get the relation between the roots and the coefficients. We say that the coefficients can be said as sum of roots and product of roots.

If p, q are roots of $a{{x}^{2}}+by+c=0$ Then
$p+q=-\dfrac{b}{a}$ and $pq=c$
p, q are roots of ${{x}^{2}}-\left( p+q \right)x+pq=0$
Given in question that $p=-q$
${{x}^{2}}-pq=0$