Write a quadratic equation with real number coefficients if one of the solutions in 3+4i?

Question

There are more than 1 answer right?

the book got

f(x)= x^2 - 6x + 25

Answer 1

The real number coefficients is 3 + 4i then the other root has to be 3 - 4i because the coefficient of x is minus the sum of the roots and the independent term is the product of the roots and they would have imaginary parts.

So the equation is (x - 3 - 4i)(x - 3 + 4i)

= [(x - 3) - 4i ][(x - 3) + 4i]

Mathematics formula: (a + b)(a - b) = (a² - b²), (a - b)² = (a² - 2ab + b²)

= (x - 3)²- (4i)²

Imaginary numbers in i² = -1

= x² - 2(x)(3) + 3² - (-16)

= x² - 6x + 9 + 16

= x² - 6x + 25.