Question

does anyone understand how to solve quadric equations how factoring is used to solve quadratic equations. Demonstrate the process with an example.

Answer 1

The general form of the quadratic eqn is ax^2 + bx +c

Answer 2

We first take the product of a and c , keeping in mind their + or - sign

Answer 3

then we find two numbers, say p and q, such that p x q = ac and p + q = b

Answer 4

Then we substitute bx by px + qx in the eqn and then find factors

Answer 5

Understood till now???

Answer 6

for eg 2x^2 - 4x - 6
Here a=2 , b= -4 and c = -6

Answer 7

Here a x c = 2 x -6 = -12
Now we have to break up -12 so that the two factors give product -12 and sum -4
Factors of 12 can be 1 x 12, 2 x 6, 3 x 4,
Out of these, if we take the pair 2 x 6 and then modify it as 2 x -6, we get 2 x -6 = -12 and 2 + (-6) = -4
So, we can say 2x^2 -4x -6 = 2x^2 + 2x - 6x - 6 = 2x(x + 1) -6 (x + 1)
Hence 2x^2 -4x -6 = (2x - 6) (x + 1)

Answer 8

Hope this clears up factorisation for you!!