SOLUTION: FInd the value of c so that the equation will have exactly one rational solution. 4p^2-12p+c=0

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Question 678342: FInd the value of c so that the equation will have exactly one rational solution.
4p^2-12p+c=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The discriminant b%5E2+%26%238722%3B+4ac can be used to determine the number and type of solutions a quadratic equation has the following types of solutions

Discriminant....................................................Number and Type of Solutions
Positive, and the square of an integer..............2 rational solutions
Positive, but not the square of an integer.........2 irrational solutions
Zero .....................................................................1 rational solution
Negative..............................................................2 non-real complex solutions

given:
4p%5E2-12p%2Bc=0
use discriminant to find c
0+=+b%5E2+-+4ac....in this case we have 1 rational solution
0+=+%2812p%29%5E2+-+4%2A4c
0+=+144p%5E2+-+16c
16c+=+144p%5E2+
c+=+144p%5E2%2F16+
c+=+9p%5E2