Answer:
The solutions of the equation are:
4/3 and 5/8
Explanation:
To get the solution of the equation, we can either solve it algebraically or graphically.
1- algebraic solution:
The general form of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
24x² - 47x + 20 = 0
By comparison, we can find that:
a = 24
b = -47
c = 20
Now, to get the roots, we will use the quadratic equation shown in the attached image.
Substituting in the equation, we would find that:
either x = [tex] \frac{-(-47) + \sqrt{(-47)^2-4(24)(20)} }{2(24)} = \frac{4}{3} [/tex]
or x = [tex] \frac{-(-47) - \sqrt{(-47)^2-4(24)(20)} }{2(24)} = \frac{5}{8} [/tex]
2- graphical solution:
To get the solution means to get the values of the x-intercepts.
Graphing the function (see attached image), we would find that the solutions are:
0.625 which is equivalent to 5/8
and 1.3333 which is equivalent to 4/3
Hope this helps :)
