SOLUTION: Use the discriminant to describe the roots of the equation: 16x^2=25 It seems like there are a few numbers missing. What do I do?

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Question 185377This question is from textbook saxon algebra 2
: Use the discriminant to describe the roots of the equation: 16x^2=25
It seems like there are a few numbers missing. What do I do? This question is from textbook saxon algebra 2

Found 3 solutions by Alan3354, feliz1965, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
16x^2=25
It seems like there are a few numbers missing. What do I do?
Any "missing" numbers are zeroes.
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16x^2 + 0x - 25 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 16x%5E2%2B0x%2B-25+=+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=%280%29%5E2-4%2A16%2A-25=1600.

Discriminant d=1600 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+1600+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+1600+%29%29%2F2%5C16+=+1.25
x%5B2%5D+=+%28-%280%29-sqrt%28+1600+%29%29%2F2%5C16+=+-1.25

Quadratic expression 16x%5E2%2B0x%2B-25 can be factored:
16x%5E2%2B0x%2B-25+=+%28x-1.25%29%2A%28x--1.25%29
Again, the answer is: 1.25, -1.25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B0%2Ax%2B-25+%29

Answer by feliz1965(151) About Me  (Show Source):
You can put this solution on YOUR website!
Use the discriminant to describe the roots of the equation: 16x^2=25
It seems like there are a few numbers missing. What do I do?
Subtract 25 from both sides.
16x^2 - 25 = 0
This tells me that a = 16, b = 0 and c = -25
When a variable is missing, replace that variable with 0.
Here is the discriminant: b^2 - 4ac
We now plug and chug.
Can you finish now?


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Use the discriminant to describe the roots of the equation: 16x^2=25
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Rearrange:
16x^2 + 0x -25 = 0
a = 16
b = 0
c = -25
================
discriminant = b^2 - 4ac
0^2 - 4*16*-25 = 1600
-----------------------
Since 1600 is greater than zero there are two unequal Real Numbers.
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Cheers,
Stan H.