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What are the zeros of the function f(x)=(x^2-13x+40)(x^2-2x+3)

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Explanation:

To find the zeros of the function f(x), we need to find the values of x that make f(x) equal to zero.

f(x) = (x^2 - 13x + 40)(x^2 - 2x + 3)

Setting f(x) equal to zero, we can use the zero product property to solve for x:

(x^2 - 13x + 40)(x^2 - 2x + 3) = 0

Either (x^2 - 13x + 40) = 0 or (x^2 - 2x + 3) = 0.

Solving for the first equation, we can use the quadratic formula:

x = [13 ± √(13^2 - 4(1)(40))] / 2(1)

x = [13 ± √(169 - 160)] / 2

x = [13 ± √9] / 2

So, the solutions for the first quadratic equation are x = 8 and x = 5.

Solving for the second equation, we can again use the quadratic formula:

x = [2 ± √(2^2 - 4(1)(3))] / 2(1)

x = [2 ± √4] / 2

So, the solutions for the second quadratic equation are x = 1 and x = 2.

Therefore, the zeros of the function f(x) are x = 8, x = 5, x = 1, and x = 2.

User Manos Dilaverakis
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