Determine which consecutive integers do not have a real zero of f(x) = x^3 + 5x^2 - x - 6 between them.
integers to have a real root in between them, the values of the polynomial on each integer should have different signs. It is because the graph crosses the x-axis in the range.
A. f(-6) = -36, f(-5) = -1, No root between them.B. f(-5) = -1, f(-4) = 14, Has a root between them. C. f(-2) = 8, f(-1) = -1, Has a root between them.D. f(1) = -1, f(2) = 20, Has a root between them.
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Answer with Step-by-step explanation:
A function f(x) is said to have a real root in an interval (a,b) if value of the function at a and b have opposite signs.
f(x)=x³+5x²-x-6
A. f(-6) = -36, f(-5) = -1
Hence, f(x) has no real root between (-6,-5)
B. f(-5) = -1, f(-4) = 14
Hence, f(x) has a root between them.
C. f(-2) = 8, f(-1) = -1
Hence, (x) has a root between them.
D. f(1) = -1, f(2) = 20
Hence, f(x) has a root between them.
Hence, correct option is:
a. (-6,-5)