1. ## repeated roots

here's the question: the following equation has repeated roots. find the value of the constant p leaving your answer in exact form:

$\displaystyle px^2 - 5x + p = 0$

could someone show me the method to figure that out please?

thanks

ps the answer is $\displaystyle p = \pm \frac{5}{2}$

2. ## Quadratic with repeated roots

Hello mark
Originally Posted by mark
here's the question: the following equation has repeated roots. find the value of the constant p leaving your answer in exact form:

$\displaystyle px^2 - 5x + p = 0$

could someone show me the method to figure that out please?

thanks

ps the answer is $\displaystyle p = \pm \frac{5}{2}$
It's worth learning that the quadratic equation $\displaystyle ax^2+bx+c=0$ has repeated roots if and only if the discriminant is zero. That means $\displaystyle b^2 - 4ac = 0$

So here: $\displaystyle a = p, b = -5$ and $\displaystyle c = p$. And when we plug these in to $\displaystyle b^2-4ac = 0$, we get:

$\displaystyle 25-4\times p \times p = 0$

$\displaystyle \Rightarrow 4p^2 = 25$

$\displaystyle \Rightarrow p^2 = \frac{25}{4}$

$\displaystyle \Rightarrow p = \pm\frac52$

3. You know that $\displaystyle px^2 - 5x + p = 0$ has one repeated root.

What does this tell you about the discriminant?