4. (a) if (x + 1) and (x + 2) are both factors of f(x) = x*-2x3-9x2 + 2x + 8, find the other two factors. Plot f(x)using Geogebra or any application to observe all roots (b) Given (x + 1) and (x – 2) are factors of f(x) = 6x* - x3 + ax² – 6x + b, find a and b, and factorise f(x) completely. %3D
4. (a) if (x + 1) and (x + 2) are both factors of f(x) = x*-2x3-9x2 + 2x + 8, find the other two factors. Plot f(x)using Geogebra or any application to observe all roots (b) Given (x + 1) and (x – 2) are factors of f(x) = 6x* - x3 + ax² – 6x + b, find a and b, and factorise f(x) completely. %3D
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
4(a) and 4(b)
Transcribed Image Text:2. Using the remainder theorem, find the remainder for each of the following
division:
(a) (2u3 + 4u2 -u+ 1) + (u-5)
(b) (x³ + 2x2 + 3x + 4) (x + 2)
(c) (x* + x3- 2x2- 2x) + (2x + 1)
3. Find k, given g(x) is a factor of p(x):
(a)
pla): 0
p(x) = x3-2x +k
g(x) = x-13:
(b)
g(x) = x+ 1;
p(x) = x5-x - kx3 + 3x +3
4. (a) if (x +1) and (x + 2) are both factors of f(x) = x-2x3-9x2 + 2x + 8, find the
other two factors. Plot f(x)using Geogebra or any application to observe all roots.
(b) Given (x + 1) and (x- 2) are factors of f(x) = 6x4- x³ + ax2 – 6x +b, find a and
b, and factorise f(x) completely.
5. Given f(x) = 2x3 – 3x2 - 8x- 3, find the remainder when f(x) divided by
(a)
x - 1
(b)
x +3
(c)
2x +1
Which among (x – 1), (x + 3) and (2x + 1) is a factor of f (x)? Find the other factor/fac
6. The expression 2x3 + ax² + bx + 6 is exactly divisible by (x – 2) and on division by (x + 1
gives a remainder of -12. Calculate the value of a and b and factorise the expression
completely.
7. Given x3 - 3x2 - 4x + 16 = (x – 2)(x + 3)(x - c) + Px +Q, find P,Q and c.
8. (a) Three factors of x* + ax³ + bx² +x +c are x,x +1 and x- 1. Find a, b and c.
(b) Given m(x) = x³ + px² + qx +r. When m(x) is divided by x,x- 2 and x+3, the
remainder is 4. Find p,q and r.
9.
Find the remainder when polynomial 3x100 + 5x85-4x38+ 2x17-6 is divided by x + 1.
10. Given p(x) = x* + 2x2 + 1 and i is a double root of p(x). Write p(x) as a product of
linear factors.
11. i and -2i are two zeroes of p(x) = x6 -2x5+ 2x* -10x3-11x2-8x-12. Find the
other zeroes and write p(x) as a product of linear factors.
Expert Solution
Step 1
Part(a)
We have and are factors of
Now,
and are factors, therefore is also a factor.
Now, dividing by we get:
Step by step
Solved in 4 steps with 3 images
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