Question

Write a quadratic equation whose factors are 4+3i and 4-3i.

Answer 1

`y=x^2-8x+25`

Explanation:

To answer this question, we will work backwards.

We know that a factor is 4+3i. This means that:

`(x-(4+3i))=0`

Hence, we will eliminate the imaginary and convert this into standard form.

First, distribute the negative:

`x-4-3i=0`

Add 3i to both sides:

`x-4=3i`

Square both sides:

`(x-4)^2=(3i)^2`

Expand:

`x^2-8x+16=9(-1)=-9`

Add 9 to both sides:

`x^2-8x+25=0`

Hence, our quadratic equation is:

`y=x^2-8x+25`

Notes:

We will get the same equation if we use (4-3i). This is because we square the (3i) regardless of its sign, making it positive.