SOLUTION: Hi, i am having trouble finding the answer to this: The following equations have repeated roots. find the value(s) of the constant p leaving your answer(s) in exact form. (p

Question 159293: Hi,
i am having trouble finding the answer to this:
The following equations have repeated roots. find the value(s) of the constant p leaving your answer(s) in exact form.
(p-1)x^2 + 6x + (p+7) = 0
i have been trying to figure it out for a while now and i have looked in the text book and the answers are -8 and 2, but i want to know how i can get these answers.
Thanks.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: repeated roots simply mean that the roots are equal. This only happens when the discriminant D is zero

Looking at , we see that , and

Start with the discriminant formula

Plug in (since the roots repeat themselves), , and

Square 6 to get 36

FOIL

Distribute

Combine like terms.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for p

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Rewrite as

Add to to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the answers are or

This means that if or , then the equation will have repeated roots.
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