SOLUTION: im really stuck on this question the roots of the quadratic equation x^2 + 4x - a= 0 are b+1 and b-3. Find the values of a and b. thnks :)

Question 355091: im really stuck on this question
the roots of the quadratic equation x^2 + 4x - a= 0 are b+1 and b-3. Find the values of a and b.
thnks :)

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
One form of a quadratic equation is:

In this form and are the two roots of the quadratic equation. This is the form which is often used when solving quadratic equations.

So you equation, with its roots of b+1 and b-3, can be written in the form:

which simplifies to:

Multiplying this out (multiplying each term of one factor by each term of the other) we get:

Combining like terms we get:

Then, for reasons that should be clear soon, I'll factor out the x from -2bx + 2x and also group the constant terms (the terms with no "x"):

In order for this equation to be the same as:

then the coefficients of the x terms must be the same:
-2b + 2 = 4
and the constant terms must be the same:

(The terms are already the same.) From
-2b + 2 = 4
we can solve for b:
-2b = 2
b = -1
Then we can use this and the equation to find a:

So a = 0 and b = -1 and your equation was
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