repeated roots

**mark** · September 7th 2009, 05:38 AM

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

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

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

thanks

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

**Grandad** · September 7th 2009, 05:51 AM

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:

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

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

thanks

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

It's worth learning that the quadratic equation $ax^2+bx+c=0$ has repeated roots if and only if the discriminant is zero. That means $b^2 - 4ac = 0$

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

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

$\Rightarrow 4p^2 = 25$

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

$\Rightarrow p = \pm\frac52$

Grandad

**Defunkt** · September 7th 2009, 05:51 AM

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

What does this tell you about the discriminant?

Nevermind, grandad ahead of me ;x

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