Qn 9.
9. x =0 or x = -3/2
Step-by-step explanation:
9. Ā 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. Ā
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. Ā 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. Ā (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) =Ā±7. This implies that;
x = -2Ā±7.
x = -9 or x = 5 are the solutions to the given quadratic equation.
Qn 12.
12. Ā x =3/8 or x = -1/3.
Step-by-step explanation:
12. Ā 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. Ā 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 orĀ x = -2.71.
Qn .19
19. Ā 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;
Ā x^2 +x -20 =0.
Qn. 20
20. Ā x^2 +6x Ā =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;
Ā x^2 +6x Ā =0.
Qn. 21
21. Ā 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; Ā
x^2 -11x +24 =0.
