select the approximate values of x that are solutions to f(x)=0, where f(x)=-9^2 +8x+5

Question

i need help please and thank you

Answer 1

f(x)=-9x^2+8x+5. When f(x)=0, -9x^2+8x+5=0 or 9x^2-8x-5=0. We can use the quadratic formula for finding the roots: x=(8+sqrt(64+180))/18=(8+sqrt(244))/18=(8+2sqrt(61))/18=(4+sqrt(61))/9. The square root of 61 is a little less than the square root of 64, which is 8, so x is approximately (4+8)/9=4/3=1.3 and (4-8)/9=-4/9=-0.4. Using a calculator we can, of course, get a better value for the root of 61, and there is a method, like long division, for working out square roots. We could also use Newton's iterative method for finding solutions, starting with the approximate values 1.3 and -0.4.

Answer 2

Given -9^2 +8x+5=f(x)

When f(x)=0
-9^2 +8x+5=0
x=(8±sqrt(64+180))/18
x=(8±sqrt(244))/18
x=(8±2sqrt(61))/18
x=(4+sqrt(61))/9
x=1.3

And
x=(4+sqrt(61))/9
x=-0.42

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