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Solve f(x)=g(x). What are the points of intersection of f(x)=x^(2)-x+3;,g(x)=2x^(2)-3x-32

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Final answer:

To solve f(x) = g(x), rearrange the equations and use the quadratic formula to solve for x. The solutions are x = 5 and x = -7, giving the points of intersection of f(x) and g(x).

Step-by-step explanation:

To solve the equation f(x) = g(x), we need to find the values of x that make the two functions equal. Setting the two functions equal, we have:

x^2 - x + 3 = 2x^2 - 3x - 32

Combining like terms and rearranging, we get:

x^2 + 2x - 35 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / (2a)

Plugging in the values a = 1, b = 2, and c = -35, we get:

x = (-2 ± sqrt(2^2 - 4(1)(-35))) / (2(1))

x = (-2 ± sqrt(4 + 140)) / 2

x = (-2 ± sqrt(144)) / 2

x = (-2 ± 12) / 2

So the two solutions for x are x = 5 and x = -7. Therefore, the points of intersection of f(x) and g(x) are (5, f(5)) and (-7, f(-7)).

User Jeroen Mols
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