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

1 Answer

1 vote

Answer:


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.

User Jfoytik
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