Question

Solve the quadratic equation by factorisation method
2x²+x-300=0

Answer 1

Answer:

Consider 2x²+x-300

2×300=600

factorize 600 into two factors whose sum is 1.

i.e., 600=24×25

=> the given equation can be written as,

2x²+25x-24x-300=0

x(2x+25)-12(2x+25)=0

x-12(2x+25)=0

on equating each part to zero

we get,

x=12 or2x+25=0

=>2x=-25

=>x=-25/2

Therefore x=12,-25/2 are the roots of the equation.

Answer 2

Answer:

x = -25/2 , 12

Note:

★ The possible values of the variable which satisfy the equation are called its roots .

★ A quadratic equation can have atmost two roots .

Solution:

Here,

The given quadratic equation is ;

2x² + x - 300 = 0 .

Let's find its roots after factorizing it using middle term splitting method.

Working rule :

Split the middle term in such a way that the product of its parts is equal to the product of first term and last term .

Thus,

=> 2x² + x - 300 = 0

=> 2x² + 25x - 24x - 300 = 0

=> x(2x + 25) - 12(2x + 25) = 0

=> (2x + 25)(x - 12) = 0

=> x = -25/2 , 12

Hence,

x = -25/2 , 12