Answer:
[tex]y=x^2-8x+25[/tex]
Step-by-step explanation:
To answer this question, we will work backwards.
We know that a factor is 4+3i. This means that:
[tex](x-(4+3i))=0[/tex]
Hence, we will eliminate the imaginary and convert this into standard form.
First, distribute the negative:
[tex]x-4-3i=0[/tex]
Add 3i to both sides:
[tex]x-4=3i[/tex]
Square both sides:
[tex](x-4)^2=(3i)^2[/tex]
Expand:
[tex]x^2-8x+16=9(-1)=-9[/tex]
Add 9 to both sides:
[tex]x^2-8x+25=0[/tex]
Hence, our quadratic equation is:
[tex]y=x^2-8x+25[/tex]
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.
