Given:
[tex]p^2-12p+c=0[/tex]Required- the value of c so that the equation will have exactly one rational solution.
Explanation:
On comparing the given equation with the standard quadratic equation ax²+bx+c=0, we have:
[tex]a=1,\text{ b=-12, c=c}[/tex]For only one solution of the equation, we should have:
[tex]b^2-4ac=0[/tex]Put the values of a, b, and c, we get:
[tex]\begin{gathered} (-12)^2-4\times1\times c=0 \\ \\ 144-4c=0 \\ \\ 4c=144 \\ \\ c=\frac{144}{4} \\ \\ c=36 \end{gathered}[/tex]Final answer: The value of c is 36 so the given equation will have exactly one rational solution.
