Question

If $3+i$ is a roots of $x^2+ax+b=0$ where $a,b\in R$, then $a=$

• A. $3$
• B. $-3$
• C. $6$
• D. $-6$

Answer 1

Answer: (D)

$-6$

In a quadratic equation with real co-efficients, complex roots occurs in pairs (root and its conjugate).

For real $a,b$, given $3+i$ is a root of the equation $x^2+ax+b=0$......(1), then $3-i$ also be root of the same equation.

Now from the relation between the roots and co-efficients of (1) we get,

$(3+i)+(3-i)=-a$

or, $a=-6$.