If the equation x 2 + b x + 45 = 0 , b ∈ R has conjugate complex roots and they satisfy z + 1 = 2 10 , then

Step-by-step solution

Let z = α + i β be one of the roots of the equation x 2 + b x + 45 = 0 ,   b ∈ R . So, its other conjugate complex root will be z = α + i β ¯ = α - i β . We know that for a quadratic equation A x 2 + B x + C = 0 , the sum and product of its roots are - B A   &   C A respectively. So, the sum of roots of the given equation, α + i β + α - i β = - b 1 ⇒ 2 α = - b   . . . . . . i . Also, the product of roots of the given equ