Respuesta :
Q1 Solution:
x = 3 or x = -1
Step-by-step explanation:
x²-2x-3 = 0
In order to solve the quadratic equation by factoring, we have to determine two numbers whose sum is -2 and their product -3. By trial and error the two numbers are found to be; -3 and 1. The next step is to split the middle term by substituting it with the above two numbers found;
x²+x-3x-3 = 0
x(x+1)-3(x+1) = 0
(x-3)(x+1) = 0
Finally we apply the zero Product Property :
If ab = 0 then a = 0 or b = 0
This implies;
x-3= 0 or x+1 = 0
x = 3 or x = -1 are the solutions to x²-2x-3 = 0
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 are the solutions to the given quadratic equation.
Answer to Q1:
{3,-1}.
Step-by-step explanation:
We have give an equation.
x²-2x-3 = 0
We have to find the solution of given equation.
We use method of factorization to solve this.
Splitting the middle term of given equation so that the sum of two term should be -2 and their product be -3, we have
x²-3x+x-3 = 0
Taking common, we have
x(x-3)+1(x-3) = 0
Taking (x-3) as common, we have
(x-3)(x+1) = 0
Applying Zero-Product Property to above equation, we have
x-3 = 0 or x+1 = 0
x = 3 or x = -1
Hence, the solution of given equation is {3,-1}.
Answer to Q2:
{3,-1/2}
Step-by-step explanation:
We have give an equation.
2x²-5x-3 = 0
We have to find the solution of given equation.
We use method of factorization to solve this.
Splitting the middle term of given equation so that the sum of two term should be -5 and their product be -6, we have
2x²-6x+x-3 = 0
Taking common, we have
2x(x-3)+1(x-3) = 0
Taking (x-3) as common, we have
(x-3)(2x+1) = 0
Applying Zero-Product Property to above equation, we have
x-3 = 0 or 2x+1 = 0
x = 3 or 2x = -1
x = 3 or x = -1/2
Hence, the solution of given equation is {3,-1/2}.
Answer to Q3:
{3,5}
Step-by-step explanation:
We have give an equation.
x²-7x = -12
x²-7x+12 = 0
We have to find the solution of given equation.
We use method of factorization to solve this.
Splitting the middle term of given equation so that the sum of two term should be -7 and their product be 12, we have
x²-4x-3x+12 = 0
Taking common, we have
x(x-4)-3(x-4) = 0
Taking (x-4) as common, we have
(x-4)(x-3) = 0
Applying Zero-Product Property to above equation, we have
x-4 = 0 or x-3 = 0
x = 4 or x = 3
Hence, the solution of given equation is {3,5}
Answer to Q4:
{6,-2/3}.
Step-by-step explanation:
We have give an equation.
3x² = 16x+12
3x²-16x-12 = 0
We have to find the solution of given equation.
We use method of factorization to solve this.
Splitting the middle term of given equation so that the sum of two term should be -16 and their product be -36, we have
3x²-18x+2x-12 = 0
Taking common, we have
3x(x-6)+2(x-6) = 0
Taking (x-6) as common, we have
(x-6)(3x+2) = 0
Applying Zero-Product Property to above equation, we have
x-6 = 0 or 3x+2 = 0
x = 6 or x = -2/3
Hence, the solution of given equation is {6,-2/3}.
Answer to Q5:
{6,-4}
Step-by-step explanation:
We have give an equation.
x²-2x-24 = 0
We have to find the solution of given equation.
We use method of factorization to solve this.
Splitting the middle term of given equation so that the sum of two term should be -2 and their product be -24, we have
x²-6x+4x-24 = 0
Taking common, we have
x(x-6)+4(x-6) = 0
Taking (x-6) as common, we have
(x-6)(x+4) = 0
Applying Zero-Product Property to above equation, we have
x-6 = 0 or x+4 = 0
x = 6 or x = -4
Hence, the solution of given equation is {6,-4}.
Answer to Q6:
{4/3,-1}
Step-by-step explanation:
We have give an equation.
3x² = x+4
3x²-x-4 = 0
We have to find the solution of given equation.
We use method of factorization to solve this.
Splitting the middle term of given equation so that the sum of two term should be -1 and their product be -12, we have
3x²-4x+3x-4 = 0
Taking common, we have
x(3x-4)+1(3x-4) = 0
Taking (3x-4) as common, we have
(3x-4)(x+1) = 0
Applying Zero-Product Property to above equation, we have
3x-4 = 0 or x+1 = 0
3x = 4 or x = -1
x = 4/3 or x = -1
Hence, the solution of given equation is {4/3,-1}.
