Estimate the real zeros of the function to the nearest tenth
f(x) = 2x^2 − 3x − 7
no reason to estimate, since the quadratic formula provides their exact values.
x = (3±√65)/4
since √65 is very close to 8, a good approximation would be
x = 11/4 or -5/4
To estimate the real zeros of a function, we need to find the x-values where the function equals zero. In this case, the function is f(x) = 2x^2 - 3x - 7.
To solve for the real zeros, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our function, a = 2, b = -3, and c = -7. Plugging these values into the quadratic formula, we get:
x = (-(-3) ± √((-3)^2 - 4(2)(-7))) / (2(2))
x = (3 ± √(9 + 56)) / 4
x = (3 ± √65) / 4
Therefore, the estimated real zeros of the function f(x) = 2x^2 - 3x - 7 are approximately:
x ≈ (3 + √65) / 4 and x ≈ (3 - √65) / 4
To find the estimates to the nearest tenth, we can evaluate these expressions using a calculator:
x ≈ 2.8 and x ≈ -0.8
Hence, the estimated real zeros of the function f(x) = 2x^2 - 3x - 7 to the nearest tenth are approximately 2.8 and -0.8.