Find the discriminant b2−4acb2-4ac, and use it to determine

2022-01-14 Answered
Find the discriminant b2−4acb2-4ac, and use it to determine the number of real solutions to the equation. a2+8=4aa2+8=4a Discriminant: Real Solution:
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Answers (1)

Vasquez
Answered 2022-02-06 Author has 460 answers

Discriminant:

a2+8=4a

a24a+8=0

D=b24ac

=(4)2418=1632=16 - Answer

Real Solution:

Solve for x:
x24x+8=0

Using the quadratic formula, solve for x.
x=4±(4)24×82=4±16322=4±162:
x=4+162orx=4162

Express 16 in terms of i.
16=116=i16:
x=4+i162orx=4i162

Simplify radicals.
16=24=4=4:
x=4+i×42orx=4i×42

Factor the greatest common divisor (gcd) of 4,4i and 2 from 4+4i.
Factor 2 from 4+4i giving 4+4i:
x=124+4 i or x=44i2

Cancel common terms in the numerator and denominator.
4+4i2=2+2i:
x=2+2i or x=44i2

Factor the greatest common divisor (gcd) of 4,4i and 2 from 44i.
Factor 2 from 44i giving 44i:
x=2+2i or x=1244i

Cancel common terms in the numerator and denominator.
44i2=22i:
x=2+2i or x=22i -  Answer 

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