SOLUTION: Find the value of c so that the equation will have exactly one rational solution. p^2-10p+c=0

Question 1115736:
Find the value of c so that the equation will have exactly one rational solution.
p^2-10p+c=0
Found 2 solutions by josgarithmetic, jim_thompson5910:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Discriminant would be 0.

Solve this.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

First I'm going to alter so that it's in a more familiar form
p^2-10p+c=0
x^2-10x+c=0 ... replace every 'p' with 'x'
1x^2-10x+c=0 ... rewrite x^2 as 1x^2
1x^2+(-10)x+c=0 ... rewrite the "1x^2-10x" as "1x^2+(-10)x"

Note how is in the form

It might be better to line up the terms like so
1x^2+(-10)x+c=0
ax^2+bx+c=0

Which helps us see that
a = 1
b = -10
c = unknown for now

Now turn to the discriminant formula

Exactly one rational solution occurs when

So we'll plug in a = 1, b = -10, and d = 0. Then we'll solve for c

(this is the final answer)

So the equation becomes

I'll leave it as an exercise for you to confirm that has exactly one solution, and to find the solution. Though this is optional, its good to practice. Hint: Quadratic Formula

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