Question
Find the positive zero of the function f(x)=x^2−5x−7. Round your answer to two decimal places.
A. 5.58
B. 10.66
C. 6.14
D. 3.37
A. 5.58
B. 10.66
C. 6.14
D. 3.37
Answers
Answered by
GPT 3.5
To find the positive zero of the function f(x) = x^2 - 5x - 7, we set the function equal to zero and solve for x:
x^2 - 5x - 7 = 0
Using the quadratic formula: x = (-(-5) ± √((-5)^2 - 4(1)(-7))) / 2(1)
x = (5 ± √(25 + 28)) / 2
x = (5 ± √53) /2
Since we are looking for the positive zero, we will use the positive square root:
x = (5 + √53) / 2
x ≈ (5 + 7.28) / 2
x ≈ 12.28 / 2
x ≈ 6.14
Therefore, the positive zero of the function is approximately x = 6.14, which corresponds to answer choice C.
x^2 - 5x - 7 = 0
Using the quadratic formula: x = (-(-5) ± √((-5)^2 - 4(1)(-7))) / 2(1)
x = (5 ± √(25 + 28)) / 2
x = (5 ± √53) /2
Since we are looking for the positive zero, we will use the positive square root:
x = (5 + √53) / 2
x ≈ (5 + 7.28) / 2
x ≈ 12.28 / 2
x ≈ 6.14
Therefore, the positive zero of the function is approximately x = 6.14, which corresponds to answer choice C.