Question

A quadratic equation with real coefficients and leading coefficient 1, has x = -bi as a root. Write the equation in general form.

Answer 1

Answer: x² + b²

Explanation:

1) Quadratic equation form, showing the two roots r₁ and r₂:

A (x - r₁)(x - r₂).

2) Coefficient 1 ⇒ A = 1

3) Complex roots ⇔ the roots are conjugate

4) r₁ = -bi ⇒ conjugate = bi = r₂

5) Replace -bi and bi for r₁ and r₂ in the general form:

[x - (-bi) ] [ x - bi] = (x + bi) (x - bi) = x² - (-bi)² = x² + b²

Answer: x² + b²

Answer 2

The general form of quadratic equation with real coefficients and leading coefficient 1, has x = -bi as a root
=> x = -b  + √ b^2 – 4 ac
                    2a

It is also written as:
=> ax^2 + bx + c = 0

Quadratic equation involves unknown numbers which is x, the numbers which a, b and c are called coeffecients.
There are also quadratic factorization where you factor the polynomial give to be able to get the value of the equation.