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

cistG

cistG

Answered question

2021-09-17

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.
x2+4x21=0

Answer & Explanation

Raheem Donnelly

Raheem Donnelly

Skilled2021-09-18Added 75 answers

Step 1
To solve the equation: x2+4x21=0
Solution:
We know, discriminant D of a quadratic equation of the form ax2+bx+c=0 is given by:
D=b24ac
Given equation is:
x2+4x21=0,a=1,b=4,c=21
D=424(1)(21)
D=16+84
D=100>0
As,D>0 given equation has two distinct real roots.
Step 2
x2+4x21=0
On simplifying further we get:
x2+4x21=0
x2+7x3x21=0
x(x+7)3(x+7)=0
(x+7)(x3)=0
(x+7)=0, or, x=3.
x={-7,3}.
Result:
Required solution is: x={−7,3}.

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