If 1 - i , is a root of the equation x2 + ax + b = 0, where a, b ∈ R, then find the values of a and b.

Question

If 1 - i , is a root of the equation x2 + ax + b = 0, where a, b ∈ R, then find the values of a and b. (A) 2, 2 (B) -2, 2 (C) -2, -2 (D) 1, 2

Tardigrade Admin · Accepted Answer

Since complex roots always occur in conjugate pair. ∴ Other conjugate root is 1+i. Sum of roots =(-a/1)=(1-i)+(1+i) ⇒ a=-2. Products of roots =(b/1)=(1-i)(1+i) ⇒ b=2

Q. If $1 - i$ , is a root of the equation $x^{2} + a x + b = 0$ , where $a, b \in R$ , then find the values of $a$ and $b$ .

$2, 2$

$- 2, 2$

$- 2, - 2$

$1, 2$

Since complex roots always occur in conjugate pair.
$∴$ Other conjugate root is $1 + i$ .
Sum of roots $= \frac{- a}{1} = (1 - i) + (1 + i)$
$\Rightarrow a = - 2$ .
Products of roots $= \frac{b}{1} = (1 - i) (1 + i)$
$\Rightarrow b = 2$

Q. If 1−i , is a root of the equation x2+ax+b=0, where a,b∈R, then find the values of a and b.

2,2

−2,2

−2,−2

1,2