The points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).
Given:
f(x) = -0.5x+2
g(x) = x³ - 5x² + 3
The point of intersection exists the point where f(x) = g(x)
x³ - 5x² + 3 = - 0.5x + 2
x³ - 5x² + 3 + 0.5x - 2 = 0
x³ - 5x² + 0.5x + 1 = 0
Factorize and estimate the value of x
Let x = 0.53 and 4.85
substitute the value of x = 0.53
f(0.53) = -0.5(0.53) + 2
f(0.53) = -0.265 + 2
f(0.53) = 1.375
If x = 4.85
f(4.85) = -0.5(4.85) + 2
f(4.85) = -2.425 + 2
f(4.85) = -0.245
Therefore, the points of intersection for the two functions and round to the nearest tenth exists (0.5, 1.4) and (4.85, -0.3).
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