QUADRATIC EQUATION: Sum of roots and product of roots

In the previous post in which we talked about finding the roots of a equation, we talked about the sum and products of a quadratic , now the proof to them is what we will be learning here.

Let's assume that a quadratic equation has two roots p and q.

Then the equation of quadratic equation must be-

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

Which on solving gives out-

x² - (p+q)x + pq = 0

Now comparing this with general form of line-

ax² + bx + c = 0

dividing by a, we get-

x² + (b/a)x + (c/a) = 0

We get-

p+q = -b/a       and     pq = c/a

If we notice we had assumed p and q to be the roots of the equation, 

Hence for any quadratic equation,

the sum of roots = (-b/a)

and

product of roots = (c/a)

Stay Tuned for the next post.

For any query comment down there.

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