Question

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

Answer 1

Answer:

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

Step-by-step 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.