# Math

Use the IVT to show that there is a root of the equation 4x^3-6x^2+3x-2=0 between 1 and 2? (please give a full answer with steps)

1. 👍 0
2. 👎 0
3. 👁 192
1. The IVT states that:
"In mathematical analysis, the intermediate value theorem states that for each value between the least upper bound and greatest lower bound of the image of a continuous function there is a corresponding point in its domain that the function maps to that value." (from Wiki)
So let
f(x)=4x^3-6x^2+3x-2
f(1)=-1
f(2)=12
and knowing that if x0 is a root, then f(x0)=0
What can you conclude using the IVT?

1. 👍 0
2. 👎 0

## Similar Questions

1. ### maths

If one of the root of the quadratic equation ax^2 + bx +c =0 is three times the other, show that 3b^2 = 16ac

2. ### calc

Show that the equation x^3-15x+c=0 has at most one root in the interval [-2,2].

1. What is the simplified form of squared root 140? A.) 4 to the square root of 35 B.) 10 to the square root of 14 C.) 2 to the square root of 70 D.) 2 to the square root of 35 Please show me how to do this Thank You

4. ### calculus

3x4 − 8x3 + 5 = 0, [2, 3] (a) Explain how we know that the given equation must have a root in the given interval. Let f(x) = 3x4 − 8x3 + 5. The polynomial f is continuous on [2, 3], f(2) = < 0, and f(3) = > 0, so by the

1. ### Alegbra 2

Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with

2. ### numerical methods

Consider a spherical storage tank containing oil. The tank has a diameter of 8 ft. You are asked to calculate the height h to which a dipstick 10 ft long would be wet with oil when immersed in the tank when it contains 6 3 ft of

3. ### Trigonometry

I'm trying to find the cosecant of 11 pi/6. The answer is -2, but I'm not sure where this came from. I thought You would flip the sine value which was sq. root of 3/2, making it 2/sq. root of three, which would then become sq.

4. ### Math

Select all possible values for x in the equation. x cubed=375. 5*the cubed root of 3 the cubed root of 375 75*the cubed root of 5 125*the cubed root of 3 I am trying to do a practice test to prepare for my real test tomorrow and I

1. ### Math simplifying mixed radicals

Please help me simplify these following mixed radicals:: and show me how you did it cause I need to learn : I don't know how to type a square root sign so I just wrote square root and the numbers infront of the square root are

2. ### Precalc/Trig 1

What equation would you use to show that the point ((square root of 11)/(6), (5/6))is on the unit circle?

3. ### Algebra

Use the quadratic formula to solve the equation. Give exact answers: 2x^2 -1 = 6x. The choices are: a) -3 + square root(7)/2, -3 - square root(7)/2 b) 3 + square root(11)/2, 3 - square root(11)/2 c) 3 + square root(7)/2, 3 -

4. ### Math - Calculus

Show that the equation x^3-15x+c=0 has at most one root in the interval [-2,2].