Question

If 3+i is a root of the equation x2 + ax + b = 0 then a is​

Answer 1

(I+3)^2=2x+ax+b=0

i^2+6i+9

i^2+3i+3i+9

i(i+3) +3(i+3)

(i+3)(i+3)=0

i= -3

Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

1. If u+ iv is a root of the quadratic equation

$a {x}^{2} + bx + c = 0$

Then u - iv is also a root of the above quadratic equation

2. Sum of the zeroes of the quadratic equation

$a {x}^{2} + bx + c = 0$

is $\displaystyle \: - \frac{b}{a}$

GIVEN

3+i is a root of the equation

${x}^{2} - ax + b = 0$

Then 3- i is a root of the above equation

So

$\displaystyle \: 3 + i + 3 - i = - \frac{ - a}{1}$

$\implies \: a = 6$

$\red { \fbox{ HENCE \: \: \: \: a = 6 \: \: }}$