Use the intermediate value theorem for polynomials to show t

Use the intermediate value theorem for polynomials to show that each polynomial function has a real zero between the numbers given. f(x) = 2x^4-4x^2 +4x-8;1 and2

Solution

f(x) = 2x^4 - 4x^2 + 4x - 8

the intermediate value theorem states that, if the function is continuous, and it is negative at one point in an interval and positive in another point in that interval, then it must be 0 somewhere in between

f(x) is contnous as it is a polynomial

Now find f(1) = 2*1 - 4*1 + 4*1 -8 = 2 -4 + 4 -8 = -6

f(2) = 2*(2)^4 - 4*(2)^2 + 4*2 - 8

= 2*16 - 4*4 + 8 - 8

= 32 - 16

= 16

since the equation is continuous and it is negative at x = 1, and it is positive at x =2, the equation must cross the x-axis somewhere in between.