f(x)=x(4x+9)(x-2)(2x-9)(x+5) has zeros at x=-5,x=-(9)/(4),x=0,x=2, and x=(9)/(2). What is the sign of f on the interval 0

Question

f(x)=x(4x+9)(x-2)(2x-9)(x+5) has zeros at  x=-5,x=-(9)/(4),x=0,x=2, and  x=(9)/(2). What is the sign of  f on the interval  0 < x < 2 ? Choose 1 answer: (A)  f is always positive on the interval. (B)  f is always negative on the interval. (C)  f is sometimes positive and sometimes negative on the interval.

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Factors Sign Analysis: Since f(x) is a product of factors, the sign of f(x) on the interval 0 < x < 2 depends on the sign of each factor in that interval.Consideration of Zeros: The zero at x=0 doesn't affect the interval 0 < x < 2, because we're looking at values of x that are greater than 0.Endpoint Consideration: The zero at x=2 is the endpoint of the interval, so we only consider values of x that are less than 2.Positive Factors: The factors (4x+9), (x-2), (2x-9), and (x+5) are all positive for values of x in the interval 0 < x < 2, because their zeros are outside this interval.Conclusion: Since all factors are positive in the interval 0 < x < 2, the function f(x) is always positive on this interval.

$f(x)=x(4 x+9)(x-2)(2 x-9)(x+5)$ has zeros at $x=-5, x=-\frac{9}{4}, x=0, x=2$ , and $x=\frac{9}{2}$ . $\newline$ What is the sign of $f$ on the interval \( 0

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f(x)=x(4x+9)(x−2)(2x−9)(x+5) f(x)=x(4 x+9)(x-2)(2 x-9)(x+5) f(x)=x(4x+9)(x−2)(2x−9)(x+5) has zeros at x=−5,x=−94,x=0,x=2 x=-5, x=-\frac{9}{4}, x=0, x=2 x=−5,x=−49​,x=0,x=2, and x=92 x=\frac{9}{2} x=29​.\newlineWhat is the sign of f f f on the interval \( 0

$f(x)=x(4 x+9)(x-2)(2 x-9)(x+5)$ has zeros at $x=-5, x=-\frac{9}{4}, x=0, x=2$ , and $x=\frac{9}{2}$ . $\newline$ What is the sign of $f$ on the interval \( 0