Question

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

Answer 1

Given:

`p^2-12p+c=0`

Required- the value of c so that the equation will have exactly one rational solution.

Step-by-step explanation:

On comparing the given equation with the standard quadratic equation ax²+bx+c=0, we have:

`a=1,\text{ b=-12, c=c}`

For only one solution of the equation, we should have:

`b^2-4ac=0`

Put the values of a, b, and c, we get:

`\begin{gathered} (-12)^2-4*1* c=0 \\ \\ 144-4c=0 \\ \\ 4c=144 \\ \\ c=(144)/(4) \\ \\ c=36 \end{gathered}`

Final answer: The value of c is 36 so the given equation will have exactly one rational solution.