Question

It is given that 2+i is a root of the quadratic equation x^2+ax+b=0

Find the values of the real numbers a and b.

Answer 1

a = - 4 and b = 5

complex roots occur in conjugate pairs, hence

if 2 + i is a root then 2 - i is also a root and

(x - (2 + i) )(x - (2 - i) ) are the factors

= (x - 2 - i)(x - 2 + i)

= (x - 2)² - i² ( i² = - 1 )

= x² - 4x + 4 + 1

= x² - 4x + 5

compare the coefficients of x² + ax + b with x² - 4x + 5

⇒ a = - 4 and b = 5