The polynomial 2x 3 + ax 2 + bx + c is denoted by f(x). The roots

Question:

The polynomial 2x³ + ax² + bx + c is denoted by f(x). The roots of f(x) = 0 are −1, 2 and k. When f(x) is divided by x − 1, the remainder is 6.
a. Find the value of k.
b. Find the remainder when f(x) is divided by x + 2.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

ISBN: 9781108407199

1st Edition

Authors: Sue Pemberton, Julianne Hughes, Julian Gilbey

See More Books

Question Posted: Mar 09, 2023 06:52 AM

See More Questions

A collar B of weight W is attached to the spring AB and can move along the rod shown. The constant of the spring is 1.5kN/m and the spring is unstretched when en = 0. Knowing that the coefficient of...
The polynomial 2x 3 + ax 2 + bx + 6 is denoted by p(x). a. Given that (x + 2) and (x 3) are factors of p(x), find the value of a and the value of b. b. When a and b take these values, factorise p(x)...
Find a parabola y = ax2 + bx + c that passes through the point (1, 4) and whose tangent lines at x = -1 and x = 5 have slopes 6 and - 2, respectively.
Onefifth of a hive of bees flew to the Kadamba flower; one-third flew to the Silandhara; three times the difference of these two numbers flew to an arbor, and one bee continued flying about,...
The U.S. Federal Bureau of Investigation publishes annual crime rates for each state and the District of Columbia in the document Crime in the United States. Those rates, given per 1000 population,...
At March 31 Streuling Enterprises, a merchandising firm, had an inventory of 38,000 units. Sales, in units, have been budgeted as follows for the next four months: April...................... 60,000...
Listed below are selected financial data from the accounting records of Retro Furniture Pty Ltd for the year ended 30 June 2022. Required Prepare an income statement for the year ended 30 June 2025....
The pharmacist at Arnold Palmer Hospital, Wende Huehn- Brown, receives 12 requests for prescriptions each hour, Poisson distributed. It takes her a mean time of 4 minutes to fill each, following a...
Consider various U.S. Treasury bonds that each pay a 5% annual coupon rate and have a face value of $1000. (a) Complete the table below. Show your work. Years to Maturity Yield-to-Maturity Current...
Figure 9.8 shows an ER schema for a database that may be used to keep track of transport ships and their locations for maritime authorities. Map this schema into a relational schema, and specify all...
The polynomial x 3 5x 2 + 7x 3 is denoted by p(x). a. Find the quotient and remainder when p(x) is divided by (x 2 2x 1). b. Use the factor theorem to show that (x 3) is a factor of p(x).
a. It is given that x + 1 is a common factor of x 3 + px + q and x 3 + (1 p)x 2 + 19x 2q. Find the value of p and the value of a. b. When p and q have these values, factorise x 3 + px + q and x 3 +...
1. Calculate the probability of at most 25 successes for a binomial random variable of 50 trials with a 45% probability of success. 2. Calculate the probability of at least 40 successes for a...
5. dy For the differential equation dx 2 I a. Draw the slope field for the differential equation. b. Graph the particular solution passing through the point (-1, 1). 6. c. Solve the differential...
An advantage when one corporation controls another is that the controlling entity's management has the ability to transfer resources between the two legal entities as needed. For example, the...
1. Determine the amount of (NH4)2SO4, in kilograms, to be supplied in a fermentation medium where the desired final cell concentration is 30 g 1 in a 10 I culture volume. Assume that the cells are...
According to Boldt, How do many states' laws potentially conflict with federal law governing the confidentiality of substance abuse treatment information? Please use link to access article:...
What are the physiological adaptations in respiratory systems across different organisms, from unicellular microorganisms to complex multicellular organisms, reflecting diverse environmental niches...
The R for a highway curve (arc definition) will be rounded off to the nearest larger multiple of 100 ft. Field conditions require M to be approximately 30 ft to avoid an embankment. The PI = 94 +...
What are the before image (BFIM) and after image (AFIM) of a data item? What is the difference between in-place updating and shadowing, with respect to their handling of BFIM and AFIM?
The following table summarises the number of tomatoes produced by the plants in the plots on a farm. a. Calculate an estimate of the mean number of tomatoes produced by these plots. b. The tomatoes...
On Monday, a teacher asked eight students to write down a number, which is denoted by x. On Tuesday, when one of these students was absent, they asked them to add 1 to yesterdays number and write it...
Eighty candidates took an examination in Astronomy, for which no candidate scored more than 80%. The examiners suggest that five grades, A, B, C, D and E, should be awarded to these candidates, using...
2. Entrepreneurial leaders are important for the sustainability of organizations. State and explain four (4 ) things that differentiate the entrepreneurial leader ship from other leader hip styles....
1) Amihan constructs a 3-storey building of which it currently rents out 1 floor and occupies the other 2 floors. The floors could not be sold separately. 2) Amihan bought several properties in...
explain The program is designed to equip accounting and finance professionals with the strong critical thinking, problem-solving and technology skills needed to advance business strategy

The polynomial 2x 3 + ax 2 + bx + c is denoted by f(x). The roots

Question:

Step by Step Answer:

a If the roots of fx are 1 2 and k then we can write fx as fx 2x1x2xk Expanding the righthand side u...View the full answer

Cambridge International AS & A Level Mathematics Pure Mathematics 2 & 3 Coursebook

Students also viewed these Mathematics questions