Question

Given the polynomial f(x) = -4x2 + 5x + 7, what is the smallest positive integer a such that the Intermediate Value

Theorem guarantees a zero exists between 0 and a?

Answer 1

here the smallest positive no be (0,-14)

Explanation:

The computation is shown below:

Here we put the value of x as 0, 1,2, 3

And solve the polynomial

Given that

-4x^2 + 5x + 7

Now

x = 0

So,

= -4(0)^2 + 5(0) + 7

= 0 + 0 + 7

= 7>0

x = 1

= -4(1)^2 + 5(1) + 7

= -4 + 5 + 7

= 8>0

x = 2

= -4(2)^2 + 5(2) + 7

= -16 + 17

= 1>0

x = 3

= -4(3)^2 + 5(3) + 7

= -36 + 15 + 7

= -14>0

So, here the smallest positive no be (0,-14)