Question

factorise:6x^2+7x-20​

Answer 1

Solution:

6x^2 + 7x - 20

6x^2 + (15 - 8)x - 20

6x^2 + 15x - 8x - 20

3x (2x + 5) - 4 (2x + 5)

(2x+5) (3x-4)

Now,

• 2x = -5
• x = -5/2

And,

• 3x = 4
• x = 4/3

Answer 2

Concept

Given a quadratic equation ax^2 + bx + c = 0, in order to factorise it we need to split the middle term b such that, the coefficient of the two middle terms after splitting equals to a*c.

Given

6x^2+7x-20​

Find

we need to factorise the given expression

Solution

We have

6x^2 + 7x - 20

here, 20*6 = 120

120 is also the product of 15 and 8 and also 15 - 8 =7

Thus, we can right 7x as follows

6x^2 + (15 - 8)x - 20

= 6x^2 + 15x - 8x - 20

Taking common terms out we get

3x (2x + 5) - 4 (2x + 5)

= (2x+5) (3x-4)

Thus,

2x + 5 = 0

x = -5/2

And,

3x - 4 = 0

x = 4/3

Thus, after factorisation 6x^2+7x-20​ becomes (2x+5) (3x-4) and we get x = -5/2 , 4/3 as its roots.

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