Question

Asked Jan 16, 2020

1 views

Show that a cubic polynomial can have at most three real zeros.

Step 1

Suppose that the polynomial

Step 2

Since the polynomials are continuous and differentiable on real numbers so using Roll’s theorem which says that between any two zeros of a differentiable function there exist a zero of its derivative. So,

Step 3

Similarly using Roll’s t...

Tagged in

Find answers to questions asked by student like you

Show more Q&A

Q: The curves y = x2 + ax + b and y = cx - x2 have a common tangent line at the point (1, 0). Find a, b...

A: Given are the two curves with a common tangent at the point (1,0)

Q: Graph the upper branch of the hyperbola y2 - 16x2 = 1

A: The given equation of hyperbola is:

Q: Using the definition, calculate the derivatives of the functions in Exercises 1–6. Then find the val...

A: Hey, since there are multiple questions posted, we will answer first two questions. If you want any ...

Q: find an equation for a circle with center (2,-1) that passes through (5,4).

A: Given a circle with center (2,-1) that passes through (5,4).

Q: Find dy/dx if a. y = (sin-1 x)2 b. y = sin-1 (1/ x) .

A: a.The given function is y = (sin–1 x)2.

Q: Determine how much time is required for a $500 investment to double in value if interest is earned a...

A: The amount after t years is given by the formula,

Q: If u is a differentiable function of x, how do you find (d/dx)(un) if n is an integer? If n is a rea...

A: Consider n as an integer or a real number.

Q: Express the limit lim E (3(x;)° – 5(x; )*)A¤; over [2, 6] as an integral. i=1 Provide a, b and f(x) ...

A: Given the Riemann sum,

Q: find the domain and range g(x) = sin (2/(5x-3))

A: Given,