Find the discriminant of each equation and determine whether the equation has (1) two nonreal complex solutions, (2) one real solution with a multiplicity of 2, or (3) two real solutions. Do not solve the equations. 7x^{2} - 2x - 14 = 0

Lewis Harvey

Lewis Harvey

Answered question

2021-06-03

Find the discriminant of each equation and determine whether the equation has (1) two nonreal complex solutions, (2) one real solution with a multiplicity of 2, or (3) two real solutions. Do not solve the equations. 7x22x14=0

Answer & Explanation

tabuordy

tabuordy

Skilled2021-06-04Added 90 answers

Step 1
We know that, for a standard form of quadratic ax2+bx+c=0, the value of discriminant D is calculated as
D=b24ac...(1)
Now,
If D>0, then both the roots of the equation must be real and distinct.
If D=0, then both the roots must be real and equal.
If D<0, then both the roots must be imaginary.
Step 2
We have the given quadratic equation as
7x22x14=0...(2)
On comparing the equation (2) with standard equation ax2+bx+c=0, we get the result as
a=7,b=2 and c=14
On using equation (1), we get the discriminant of equation 7x22x14=0 as
D=(2)2(4)(7)(14)
D=4+392
D=396
D>0
Hence, there will be two real and distinct solution.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?