SOLUTION: My paper says: Find the value of the discriminant for 9x^2+1=6x. Then describe the number and type of roots for the equation..... I already found the discriminant to be -72 i just

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Question 583145: My paper says: Find the value of the discriminant for 9x^2+1=6x. Then describe the number and type of roots for the equation..... I already found the discriminant to be -72 i just dont know how to do the last part
Found 2 solutions by solver91311, Alan3354:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The discriminant is:

Your quadratic in standard form



So , , and

The first thing for you to do is to write back and tell me how you managed to get out of



and how you managed to get anything involving when you didn't take a square root anywhere.

Use the following to determine the nature of the roots:

Find the Discriminant, and evaluate the nature of the roots as follows:

No calculation quick look: If the signs on and are opposite, then guaranteed.

Two real and unequal roots. If is a perfect square, the quadratic factors over (the rationals).

One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. Presuming rational coefficients, the root will be rational as well.

A conjugate pair of complex roots of the form where is the imaginary number defined by

John

My calculator said it, I believe it, that settles it
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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the value of the discriminant for 9x^2+1=6x. Then describe the number and type of roots for the equation..... I already found the discriminant to be -72 i just dont know how to do the last part
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Disc = 6^2 - 4*9*1 = 0
Not -72
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Disc = 0 --> 2 real roots, same value
For this eqn, x = 1/3, 1/3
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Or, x = 1/3 multiplicity 2
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 9x%5E2%2B-6x%2B1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-6%29%5E2-4%2A9%2A1=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-6%29%29%2F2%5C9.
Expression can be factored: 9x%5E2%2B-6x%2B1+=+%28x-0.333333333333333%29%2A%28x-0.333333333333333%29

Again, the answer is: 0.333333333333333, 0.333333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-6%2Ax%2B1+%29