Which of the following equations has the sum of its roots as 3?

Solution:

Given the following quadratic equations

(a) x2 + 3x − 5 = 0

(b) −x2 + 3x + 3 = 0

(c) $\sqrt{2} x^{2}-\frac{3}{\sqrt{2}} x-1=0$

(d) $3 x^{2}-3 x-3=0$

We are to find out which of the above equations has sum of roots = 3.

The sum of the roots of the quadratic equation $a x^{2}+b x+c=0$ is given by $-\frac{b}{a}$.

For given equation (a)

a = 1, b = 3, c = −5

Sum of roots $=-\frac{3}{1}=-3$

For given equation (b)

a = −1, b = 3, c = 3

Sum of roots $=-\frac{3}{-1}=3$

For given equation (c)

$a=\sqrt{2}, b=-\frac{3}{\sqrt{2}}, c=-1$

Sum of roots $=-\frac{\left(-\frac{3}{\sqrt{2}}\right)}{\sqrt{2}}=\frac{3}{2}$

For given equation (d)

a = 3, b = −3, c = −3

Sum of roots $=-\frac{(-3)}{3}=1$

The sum of roots of equation $(b)$ is 3

Hence option (b) is correct.