Question

Help it’s due tomorrow !!!

Answer 1

Answer to Q1:

x = 3 or x = -1

Step-by-step explanation:

We have given an equation.

x²-2x-3 = 0

We  have to solve above equation by factoring.

Splitting the middle term of above equation so that the sum of two term should be -2 and product be -3.

x²-3x+x-3  =  0

x(x-3)+1(x-3)  = 0

(x-3)(x+1) = 0

Zero Product Property :

If ab = 0 then a  = 0 or b  = 0

Applying Zero Product Property,we have

x-3= 0 or x+1 = 0

x = 3 or x = -1 which is the solution of x²-2x-3 = 0

Answer to Q2:

x  = 1/2 or x  =  3

Step-by-step explanation:

We have given an equation.

2x²-5x-3  =0

We  have to solve above equation by factoring.

Splitting the middle term of above equation so that the sum of two term should be -5 and product be -6.

2x²-6x+1x-3  = 0

2x(x-3)-1(x-3) = 0

(2x-1)(x-3)   = 0

Applying Zero Product Property,we have

2x-1 = 0 or x-3 =  0

2x = 1 or x =  3

x  = 1/2 or x  =  3 which is solution of given equation.

Answer to Q3:

x = 4 or x = 3

Step-by-step explanation:

We have given an equation.

x²-7x = -12

x²-7x+12 = 0

We  have to solve above equation by factoring.

Splitting the middle term of above equation so that the sum of two term should be -7 and product be 12.

x²-4x-3x+12 = 0

x(x-4)-3(x-4)  = 0

(x-4)(x-3) = 0

Applying Zero Product Property,we have

x-4 = 0 or x-3 = 0

x = 4 or x = 3 which is solution of given equation.

Answer to Q4:

x = -2/3 or x = 6

Step-by-step explanation:

We have given an equation.

3x² = 16x+12

3x²-16x-12 = 0

We  have to solve above equation by factoring.

Splitting the middle term of above equation so that the sum of two term should be -16 and product be -36.

3x²-18x+2x-12 = 0

3x(x-6)+2(x-6) = 0

(3x+2)(x-6) = 0

Applying Zero Product Property,we have

3x+2 = 0 or x-6 =0

3x = -2 or x = 6

x = -2/3 or x = 6 which is solution of given equation.

Answer to Q5:

x = 6 or x = -4

Step-by-step explanation:

We have given an equation.

x²-2x-24 = 0

We  have to solve above equation by factoring.

Splitting the middle term of above equation so that the sum of two term should be -2 and product be -24, we have

x²-6x+4x-24 = 0

x(x-6)+4(x-6) = 0

(x-6)(x+4) = 0

Applying Zero Product Property,we have

x-6 = 0 or x+4 = 0

x = 6 or x = -4 which is solution of given equation.

Answer to Q6:

x  = 4/3 or x  = -1

Step-by-step explanation:

We have given an equation.

3x² = x+4

3x²-x-4 = 0

We  have to solve above equation by factoring.

Splitting the middle term of above equation so that the sum of two term should be -1 and product be -12, we have

3x²-4x+3x-4 = 0

x(3x-4)+1(3x-4)  =0

(3x-4)(x+1) = 0

Applying Zero Product Property,we have

3x-4 =0 or x+1 =0

3x  = 4 or x = -1

x  = 4/3 or x  = -1 which is solution of given equation.

Answer 2

1. x=3 or x=-1

Step-by-step explanation:

1. x^2 -2x -3 =0 .

The product is -3 while the sum is -2. We determine two numbers whose product is -3 and sum -2. The two numbers are -3 and 1. The next step is to replace -2x in the equation with these two values; x^2 +x -3x -3 =0. Factoring yields; x(x+1) -3(x+1) =0. Upon simplification this becomes; (x-3)(x+1) =0. This implies that either; x-3 =0 or x+1 =0. Solving for x yields; x=3 or x=-1

Q2  Solution:

x  = -1/2 or x  =  3

Step-by-step explanation:

2x²-5x-3  =0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -5 and their product 2(-3)=-6. By trial and error the two numbers are found to be; -6 and 1. The next step is to split the middle term by substituting it with the above two numbers found;

2x²-6x+x-3  = 0

2x(x-3)+1(x-3) = 0

(2x+1)(x-3) = 0

2x+1 = 0 or x-3 =  0

2x = -1 or x =  3

x  = -1/2 or x  =  3 are the solutions of the given quadratic equation.

Q3 Soution:

x = 4 or x = 3

Step-by-step explanation:

x²-7x = -12

x²-7x+12 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -7 and their product 12. By trial and error the two numbers are found to be; -4 and -3. The next step is to split the middle term by substituting it with the above two numbers found;

x²-4x-3x+12 = 0

x(x-4)-3(x-4)  = 0

(x-4)(x-3) = 0

x-4 = 0 or x-3 = 0

x = 4 or x = 3 are the solutions of the given quadratic equation.

Q4:

x = -2/3 or x = 6

Step-by-step explanation:

3x² = 16x+12

3x²-16x-12 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -16 and their product 3(-12)= -36. By trial and error the two numbers are found to be; -18 and 2. The next step is to split the middle term by substituting it with the above two numbers found;

3x²-18x+2x-12 = 0

3x(x-6)+2(x-6) = 0

(3x+2)(x-6) = 0

3x+2 = 0 or x-6 =0

3x = -2 or x = 6

x = -2/3 or x = 6 are the solutions of the given quadratic equation.

Q5:

x = 6 or x = -4

Step-by-step explanation:

x²-2x-24 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -2 and their product -24. By trial and error the two numbers are found to be; -6 and 4. The next step is to split the middle term by substituting it with the above two numbers found;

x²-6x+4x-24 = 0

x(x-6)+4(x-6) = 0

(x-6)(x+4) = 0

x-6 = 0 or x+4 = 0

x = 6 or x = -4 are the solutions to the given quadratic equation.

Q6:

x  = 4/3 or x  = -1  

Step-by-step explanation:

3x² = x+4

3x²-x-4 = 0

In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -1 and their product -12. By trial and error the two numbers are found to be; -4 and 3. The next step is to split the middle term by substituting it with the above two numbers found;

3x²-4x+3x-4 = 0

x(3x-4)+1(3x-4)  =0

(3x-4)(x+1) = 0

3x-4 =0 or x+1 =0

3x  = 4 or x = -1

x  = 4/3 or x  = -1