Question: Let f(x) = ax 2 + bx + c, where a, b, and c are odd integers. If x is an integer, show that f(x)

Let f(x) = ax2 + bx + c, where a, b, and c are odd integers. If x is an integer, show that f(x) must be an odd integer.

x is either an even integer or an odd integer.

Step by Step Solution

★★★★★

3.37 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If x is even then ax 2 and bx are even When ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

(a) Show that the set of all functions of the form f(x) = (ax2 + bx + c) ex for a, b, c, R forms a vector space. What is its dimension? (b) Show that the derivative D[f(x)] = f(x) defines an...

Q:

Consider f(x) = Ax2 + Bx + C with A > 0. Show that f(x) 0 for all x if and only if B2 - 4AC 0.

Q:

Let f(x) = ax2 + bx + c. show that Both have the value (h/3)[a(6m2+2h2) + b(6m) + 6c]. This establishes the area formula on which the Parabolic Rule is based. f(x) dx and h 4(m) + f(m + h)]

Q:

How Can I solve these tasks ? 5. Let f (x) = x' + ax + bx + c. What requirements must be imposed on the constants a, b, and c in order that f will have: (a) a local minimum at x = 0? (b) critical...

Q:

Cant solve question 5... 5. Let f (x) = x + ax + bx + c. What requirements must be imposed on the constants a, b, and c in order that f will have: (a) a local minimum at x = 0? (b) critical points at...

Q:

16. A cubic polynomial function f is defined by f (x) = =x3+ ax + bx + c, where a, b, and c are constants. The function f has a local minimum at x = -2, and the graph of f has a point of inflection...

Q:

Knowledge & Understanding (all questions are of 4 marks) 1. Determine an equation for the function h(x) = f(x) +g(x) in each case and state the domain and range of the function. a) f(x) = x, g(x) = 3...

Q:

Legibly Printed Family/Last Name: Legibly Printed Given/FirstName: Signature: M119 Seat number: EXAM 3 14th April 2015 READ THIS: For each of the problems that begin on the next page, find the one...

Q:

Criterion for the Galois Group of an Irreducible Cubic over an Arbitrary Field Suppose K is a field and f x x ax bx c K x is irreducible so the Galois group of f x over K is either S3 or A3 a Show...

Q:

Height (meters) The figure above is the graph of a function of x, which models the height of a skateboard ramp. The function meets the following requirements. (i) At X = 0, the value of the function...

Q:

Why should an entrepreneur develop a business plan?

Q:

Using figure 4.22 as a guide, label the stages in the endospore cycle shown in the figure, and explain the events depicted. Figure 4.22 vegetative ce Core Spore coats Cortex Cell wall Cell membrane...

Q:

What form of ownership is characterized by only a very few people of the larger group assuming full responsibility for management in addition to full liability for the success of the investment

Q:

What is multicollinearity? What problems can arise because of multicollinearity?

Q:

Using the data from Problem 9, test whether the standard deviation of wait time at Wendy's is more than that at McDonald's at the a = 0.05 level of significance.

Q:

Height versus Arm Span Construct and interpret a 95% confidence interval for the population mean difference between height and arm span using the data from Problem 8. What does the interval lead us...

Q:

McDonald's versus Wendy's Construct and interpret a 95% confidence interval about M - W using the data from Problem 9. How might a marketing executive with McDonald's use this information?

Q:

6-8, As an Equity analyst you are concerned with what will happen to the required return to Universal Toddler Industries stock as market conditions change. Suppose r_RF=5%, r_M= 12%, and b_UTI=1.4....

Q:

QUESTION 14 Which of the following ratios is purely a performance ratio? current ratio times interest earned ratio return on assets ratio debt to assets ratio (debt ratio)

Q:

James Corporation is comparing two different capital structures: an all-equity plan (Plan I) and a levered plan (Plan II). Under Plan I, the company would have 144,000 shares of stock outstanding....