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Question

My teacher asked us to simplify

a (x-((-b-sqrt(b^2-4ac))/2a) (x-((-b+sqrt(b^2-4ac))/2a)

I know its quadratric equation but she said to simplify it and there is an easy way without foil and it will only take a few lines I think.

Please help . Thank You

Answer 1

The quadratic equation with roots p and q is:

(x - p)(x - q) = 0

Multiplying this out:

x^2 - (p + q)x + pq = 0

Multiplying by a:

ax^2 - a(p + q) + apq = 0 ...(1)

Compare (1) with ax^2 + bx + c = 0

The coefficients of x need to be equal:

b = - a(p + q)

p + q = - b / a

The absolute terms need to be equal:

c = apq

pq = c / a.

Your formula is a(x - p)(x - q) and is therefore identical to:

ax^2 + bx + c.