Respuesta :
Qn 9.
9. x =0 or x = -3/2
Step-by-step explanation:
9. 4x^2 +6x =0. The first step is to factor x;
x(4x+6) =0.
This implies that either;
x=0 or 4x+6 =0.
Solving for x yields;
4x =-6 which upon dividing both sides by 4 becomes x =-3/2.
x =0 or x = -3/2 are the solutions to the given quadratic equation.
Qn 10.
10. x =0 or x =3
Step-by-step explanation:
10. 7x^2 =21x.
The equation can be rewritten as;
7x^2 -21x =0.
We note that 7x is a common multiple and we factor it out;
7x(x-3)=0. This implies that either;
7x =0 or x-3 =0. Solving 7x =0 yields;
x=0. Solving x-3 = 0 yields;
x =3.
x =0 or x =3 are the solutions to the given quadratic equation
Qn 11.
11. x = -9 or x = 5
Step-by-step explanation:
11. (x+2)^2 =49.
The equation is already in factored form. The next step is to obtain square roots on both sides of the equation which yields;
(x+2) =±7. This implies that;
x = -2±7.
x = -9 or x = 5 are the solutions to the given quadratic equation.
Qn 12.
12. x =3/8 or x = -1/3.
Step-by-step explanation:
12. x+3 =24x^2.
The first step is to write the equation in the standard form;
24x^2 -x -3 =0.
The next step we make the coefficient of x^2 equal to 1 by diving all through by 24;
x^2 -(1/24)x - (1/8) =0.
Consequently, we determine two numbers whose sum is -(1/24) and their product -(1/8). By trial and error the two numbers are found to be; -(3/8) and (1/3). The equation is then re-written as;
x^2 +(1/3)x -(3/8)x -(1/8) =0. The equation is then factored as;
x(x +1/3) -3/8 (x +1/3) =0. Upon simplification this becomes;
(x -3/8)(x +1/3) =0. Implying that;
x =3/8 or x = -1/3 are the solutions to the given quadratic equation.
Qn 13.
13. x =2.5 or x = -2
We plot the individual functions using the Desmos graphing utility; an online graphing tool. Consequently we determine the x-intercept which represents the zeros of the given function;
The graphical solutions to the first equation are; x =2.5 or x = -2.
Qn. 14
The graphical solutions to the this equation are; x =3.5 or x = -1.33.
Qn. 15
The graphical solutions to the this equation are; x =0.42 or x = -7.17.
Qn. 16
The graphical solutions to the this equation are; x =3.25 or x = -2.
Qn. 17
The graphical solutions to the this equation are; x =4.5 or x = -0.67.
Qn. 18
The graphical solutions to the this equation are; x =0.46 or x = -2.71.
Qn .19
19. x^2 +x -20 =0.
Step-by-step explanation:
If 4 and -5 are the solutions to a quadratic equation, this implies;
x =4 or x = -5.
Consequently;
x -4 =0 or x +5 =0.
(x -4)(x+5) =0.
Opening the brackets and simplifying yields;
x^2 +x -20 =0.
Qn. 20
20. x^2 +6x =0
Step-by-step explanation:
If -6 and 0 are the solutions to a quadratic equation, then;
x =-6 or x = 0.
This implies that;
x +6 =0 or x =0.
Consequently;
x(x+ 6) =0
Opening the brackets and simplifying yields;
x^2 +6x =0.
Qn. 21
21. x^2 -11x +24 =0
Step-by-step explanation:
If 3 and 8 are the solutions to a quadratic equation, then;
x =3 or x = 8.
This implies that;
x -3 =0 or x -8 =0.
Consequently;
(x -3)(x -8) =0
Opening the brackets and simplifying yields;
x^2 -11x +24 =0.
Answer to Q9:
{0,-3/2}
Step-by-step explanation:
We have given an equation.
4x² + 6x = 0
We have to solve above equation for the value of x.
Taking 2x common from given equation, we have
2x(2x+3) = 0
Applying Zero-Product Property , we have
2x = 0 or 2x+3 = 0
x = 0 or 2x = -3
x = 0 or x = -3/2
Hence, the solution of given equation is {0,-3/2}.
Answer to Q10:
{0,3}
Step-by-step explanation:
We have given an equation.
7x² =21x
We have to solve above equation for the value of x.
Adding -21x to both sides of above equation, we have
7x²-21x = 21x-21x
7x²-21x = 0
Taking 7x common from above equation, we have
7x(x-3) = 0
Applying Zero-Product Property , we have
7x = 0 or x-3 = 0
x = 0 or x = 3
Hence, the solution of given equation is {0,3}.
Answer to Q11:
{5,-9}.
Step-by-step explanation:
We have given an equation.
(x+2)² = 49
We have to solve above equation for the value of x.
Taking square root to both sides of above equation, we have
√(x+2)² = √49
x+2 = ±7
Adding to -2 to both sides of above equation, we have
x+2-2 = ±7-2
x = 7-2 or x = -7-2
x = 5 or x = -9
Hence, the solution of given equation is {5,-9}.
Answer to Q12:
{1/2,-1/3}
Step-by-step explanation:
We have given an equation.
x+3 = 24x²
24x²-x-3 = 0
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 -72, we have
24x²-9x+8x-3 = 0
Taking common, we have
3x(8x-3)+1(8x-3) = 0
Taking (8x-4) as common, we have
(8x-4)(3x+1) = 0
Applying Zero-Product Property to above equation, we have
8x-4 = 0 or 3x+1 = 0
8x = 4 or 3x = -1
x = 4/8 or x = -1/3
x = 1/2 or x =-1/3
Hence, the solution of given equation is {1/2,-1/3}.
Answer to Q13:
(2.5,0) and (2,0)
Step-by-step explanation:
We have given an quadratic equation.
2x²-x-10 = 0
We have to solve above equation by method of graphing.
We have plotted the graph of given equation.
Finding the x-intercepts of equation, we have
(2.5,0) and (2,0)
Hence, x-intercepts are the solution of given equation.
Answer to Q14:
(-1.33,0) and (3.5,0)
Step-by-step explanation:
We have given an quadratic equation.
6x²-13x = 28
6x²-13x-28 = 0
We have to solve above equation by method of graphing.
We have plotted the graph of given equation.
Finding the x-intercepts of equation, we have
(-1.33,0) and (3.5,0)
Hence, x-intercepts are the solution of given equation.
Answer to Q15:
(-7.17,0) and (0.42,0)
Step-by-step explanation:
We have given an quadratic equation.
4x²+27x = 12
4x²+27x-12 = 0
We have to solve above equation by method of graphing.
We have plotted the graph of given equation.
Finding the x-intercepts of equation, we have
(-7.17,0) and (0.42,0)
Hence, x-intercepts are the solution of given equation.
Answer to Q16:
(-2,0) and (3.25,0)
Step-by-step explanation:
We have given an quadratic equation.
4x²-5x-26 = 0
We have to solve above equation by method of graphing.
We have plotted the graph of given equation.
Finding the x-intercepts of equation, we have
(-2,0) and (3.25,0)
Hence, x-intercepts are the solution of given equation.
Answer to Q17:
(-.67,0) and (4.5,0)
Step-by-step explanation:
We have given an quadratic equation.
6x²-23x = 18
6x²-23x-18 = 0
We have to solve above equation by method of graphing.
We have plotted the graph of given equation.
Finding the x-intercepts of equation, we have
(-.67,0) and (4.5,0)
Hence, x-intercepts are the solution of given equation.
Answer to Q18:
(-2.77,0) and (.46,0)
Step-by-step explanation:
We have given an quadratic equation.
-4x²-9x+5 = 0
We have to solve above equation by method of graphing.
We have plotted the graph of given equation.
Finding the x-intercepts of equation, we have
(-2.77,0) and (.46,0)
Hence, x-intercepts are the solution of given equation.
Answer to Q19:
x²+x-20 = 0
Step-by-step explanation:
We have given the solution of equation.
4 and -5
We have to find the equation of given solution.
x = 4 and x = -5
Hence, x-4 = 0 and x +5 = 0
For equation,
(x-4)(x+5) = 0
x²-4x+5x-20 = 0
x²+x-20 = 0 which is the answer.
Answer to Q20:
x²+6x = 0
Step-by-step explanation:
We have given the solution of equation.
-6 and 0
We have to find the equation of given solution.
Hence, x = -6 and x = 0
x+6 = 0 and x = 0
x(x+6) = 0
Distribute x over parentheses,
x²+6x = 0 which is the answer.
Answer to Q21:
x²-11x+24 = 0
Step-by-step explanation:
We have given the solution of equation.
3 and 8
We have to find the equation of given solution.
x = 3 and x = 8
x-3 = 0 and x-8 = 0
(x-3)(x-8) = 0
x²-3x-8x+24 = 0
Adding like terms, we have
x²-11x++24 = 0 which is the answer.
