Find all the zeros of the function f(x)=x^2-8x-9
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We have to find the zeros of the function f(x) = x^2 - 8x - 9
For this we equate f(x) to 0 and solve the quadratic equation that is obtained.
f(x) = 0
=> x^2 - 8x - 9 = 0
=> x^2 - 9x + x - 9 = 0
=> x(x - 9) +1(x - 9) = 0
=> (x - 9)(x + 1) = 0
for x - 9 = 0 , we have x = 9
for x + 1 = 0, we have x = -1
The requires zeros are x = -1 and x = 9
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Since we know that the zero of a function is any substitution of the variable that cancel the function, we'll put:
f(x) = 0
x^2-8x-9 = 0
This function has no more than 2 zeros, since its order is 2.
We'll apply quadratic formula:
x1 = [8 + sqrt(64 + 36)]/2
x1 = (8+sqrt100)/2
x1 = (8+10)/2
x1 = 9
x2 = (8-10)/2
x2 =-1
The zeros of the function are the real values x1 = 9 and x2 = -1.
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