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

ruigE

ruigE

Answered question

2021-09-30

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.
15x2+17x4=0

Answer & Explanation

Jaylen Fountain

Jaylen Fountain

Skilled2021-10-01Added 169 answers

Step 1
The quadratic equation ax2+bx+c=0 has two real different solutions if b24ac>0 .
It has two complex solutions if b24ac<0.
Step 2
The given equation is 15x2+17x4=0
By comparing with its standard form ax2+bx+c=0, it is obtained that a=15, b=17 and c=−4.
This implies that,
b24ac=(17)24(15)(4)
=289+240
=529
Since b24ac>0, the given equation has two different real solutions.
These solution can be obtained as follows.
x=b±b24ac2a
=17±5292(15)
=17±2330
=43 or 15
Thus, the solutions are 43 and 15.

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