First use the discriminant to determine whether the equation has two nonreal com

Falak Kinney

Falak Kinney

Answered question

2021-10-02

First use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. Then solve the equation.
x23x54=0

Answer & Explanation

Alannej

Alannej

Skilled2021-10-03Added 104 answers

Step 1
Given : The quadratic equation x23x54=0
we have to tell using the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions also we have to solve the given equation.
Step 2
as we know that the discriminant is given as b24ac
here x23x54=0
a=1, b=-3, c=-54
D=(3)24(1)(54)
D=(3)24(1)(54)
D=9+216
D=225
since D is a perfect square thereforeThe roots exists are real and distinct.
x=b±D2a
x=(3)±2252
x=3±152
x=3+152,3152
x=182,122
x=9, -6

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