Answer:
x² - x - 2 = 0
Step-by-step explanation:
plotting the graph of x and y,we have that the root of the equation is -1 or 2
x = -1 or 2
the eqn therefore is;
x² - (sum of the root)x + (product of the root) =. 0
x² - (-1+2)x + (-1*2) = 0
x² - x - 2 = 0
Applying the Factor Theorem, it is found that the quadratic function is:
[tex]p(x) = x^2 - x - 2[/tex]
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The Factor Theorem states that if a polynomial [tex]p(x)[/tex] has roots [tex]x_1, x_2, ..., x_n[/tex], it is described by the following equation:
[tex]p(x) = a(x - x_1)(x - x_2)...(x - x_n)[/tex]
In which a is the leading coefficient.
[tex]p(x) = a(x - (-1))(x - 2)[/tex]
[tex]p(x) = a(x + 1)(x - 2)[/tex]
[tex]p(x) = a(x^2 - x - 2)[/tex]
When x = 0, p(x) = -2, and we use this to find a.
[tex]p(x) = a(x^2 - x - 2)[/tex]
[tex]-2 = a(0^2 - 0 - 2)[/tex]
[tex]2a = 2[/tex]
[tex]a = \frac{2}{2}[/tex]
[tex]a = 1[/tex]
Thus, the quadratic function is:
[tex]p(x) = x^2 - x - 2[/tex]
A similar problem is given at https://brainly.com/question/24380382
