Review question

# When does $(p+1)x^2+4px+9=0$ have a repeated root? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7455

## Solution

Find the values of $p$ for which the equation$(p+1)x^2+4px+9=0$ has equal roots.

A quadratic equation has equal roots if and only if its discriminant is zero.

So here we require $(4p)^2 - 4(9(p+1)) = 0$. Dividing by $4$ gives \begin{align*} 4p^2 - 9(p+1) &=0 &\iff\quad&&4p^2 - 9p - 9 = 0 \\ &&\iff\quad&&(p - 3)(4p + 3) = 0 \\ &&\iff\quad&&p = 3 \ \text{or} \ p=-\tfrac{3}{4}. \end{align*}

So for these two values of $p$ (and no other values), the quadratic equation has equal roots.