# If one of the equation x2 + ax + 3 = 0 is 1, then its other root is

Question:

If one of the equation $x^{2}+a x+3=0$ is 1 , then its other root is

(a) 3
(b) −3
(c) 2
(d) 1

Solution:

Let $\alpha$ and $\beta$ be the roots of quadratic equation $x^{2}+a x+3=0$ in such a way that $\alpha=1$

Here, $a=1, b=a$ and, $c=3$

Then, according to question sum of the roots

$\alpha+\beta=\frac{-b}{a}$

$1+\beta=\frac{-a}{1}$

$\beta=-a-1$

And the product of the roots

$\alpha \cdot \beta=\frac{3}{1}$

$1 \times \beta=3$

$\beta=3$

Therefore, value of other root be $\beta=3$

Thus, the correct answer is (a)