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)