Question

1. Solve the following quadratic equations by
factorisation method :
(i) x^2-5x-36=0
​

Answer 1

Answer:

x = 9 , − 4

I hope this helped

Answer 2

Answer:

Step-by-step explanation

x^2-5x-36=0

Factoring x2-5x-36

The first term is, x2 its coefficient is 1 .

The middle term is, -5x its coefficient is -5 .

The last term, "the constant", is -36

Step-1 : Multiply the coefficient of the first term by the constant 1 • -36 = -36

Step-2 : Find two factors of -36 whose sum equals the coefficient of the middle term, which is -5 .

-36 + 1 = -35

-18 + 2 = -16

-12 + 3 = -9

-9 + 4 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -9 and 4

x2 - 9x + 4x - 36

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (x-9)

Add up the last 2 terms, pulling out common factors :

4 • (x-9)

Step-5 : Add up the four terms of step 4 :

(x+4) • (x-9)

Which is the desired factorization

Equation at the end of step

1

:

(x + 4) • (x - 9) = 0

STEP

2

:

Theory - Roots of a product

2.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.