core: 0 of 3 pts 80f 9 (9 complete) HW Sc 3.2.49 Use the intermediate value theo

Question

core: 0 of 3 pts 80f 9 (9 complete) HW Sc 3.2.49 Use the intermediate value theorem to check whether the polynomial function Px) given below has a real zero in the intervail [1,2J. tfit has a zero in the interval, approximabe the zero to two decimal plao Plx)#x5-2x2-12 Select the correct choice below and fill in the answer box with your choice if necessary O A. The polynomial function P(x) has no zero in the given interval. O B. The approximate value of zero of P(x) is. (Round to two decimal places as needed.)

Explanation / Answer

P(x) = x^5 - 2x^2 - 12

P(1) = 1^5 - 2(1)^2 - 12

= -13

P(2) = 2^5 - 2(2)^2 - 12

= 12

at x = 1 the curve is below 0

and at x = 2 the curve is above 0

so, somewhere in between curve will cross through y = 0

hence, there is a zero in the interval [1 , 2]

the approximate value of zero of P(x) is 1.79

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