Question

Very short Questions (i) Solve the equation by factorization method: 2x²+x-6=0 ​

Answer 1

Splitting the middle term

This can be solved using splitting the middle term method. Splitting the middle term is a method of factorization in which we need a x² term, x term and a constant, which are equal to 0.

Let's look at the question now, It is given that,

• $\sf{2x^2\:+\:x\:-\:6\:=\:0}$

Here We have, a x² term which is 2x², a x term which is x and a constant which is 6.

Solving using this method :

Step 1 : Multiplying the co - efficient of x² with the constant term. we get,

• $\sf{x^2\:+\:x\:-\:(6\:\times\:{2})\:=\:0}$
• $\sf{x^2\:+\:x\:+\:12\:=\:0}$

Step 2 : Taking the constant as product and co - efficient of x as sum, we get,

• Product = $\sf12$
• Sum = $\sf1$

Step 3 : Splitting the middle term process

• Refer to the attachment

Step 4 : Divide the answers by co - efficient of x², which is 2 and x.

• $\sf{\dfrac{-3}{2x}}$ and $\sf{\dfrac{+4}{2x}}$ = $\sf{\dfrac{2}{x}}$

Step 6 : Taking x term towards up,

• Refer the attachment

Step 7 : (2x - 3) (x + 2) = 0

Step 8 : Equalling both separatly with 0

• $\sf{2x\:-\:3\:=\:0}$
• $\sf{x\:+\:2\:=\:0}$

Step 9 : Solving both,

• $\sf{2x\:=\:3}$ $\implies\sf{x\:=\:{\dfrac{3}{2}}}$
• $\sf{x\:=\:-2}$

Hence, x = 3/2 and -2 is the required answer.

Answer 2

Answer:

Step-by-step explanation:

2x+2x+x+6=0

4x+x+6=0

5x+6=0

5x=0-6

5x=0

x=0÷5

x=0