Download Questions for 3.3 - Dammam Community College

Dammam Community College
MATH 011
Past Exam Questions
Section – 3.3
1. The polynomial P( x)  5x6  2 x2  4 has :
(a)
(b)
(c)
(d)
(e)
No rational zeros ←
Six rational zeros
Two rational zeros and four irrational zeros
Two rational zeros and four non complex zeros
Four rational zeros and two irrational zeros
2. If –2 is a zero of multiplicity 2 of P ( x)  3x3  6x2  Ax  B then the sum of the constants A and B is
(a)
(b)
(c)
(d)
(e)
–36
–22
31
38
25
←
3. The sum of all rational zeros of the polynomial P ( x)  6x4  5x3  7 x2  5x  1 is equal to:
5
(a) 
←
6
13
(b) 
6
7
(c) 
6
(d) 0
11
(e) 
6
4.
1
is a zero of multiplicity 2 of the polynomial P ( x)  16x4  8x3  399x2  200x  25 ; then one of the
4
following expressions is a factor of P ( x )
If
(a) 16x  25
2
(b) 25x  400
2
(c) 16x  400
2
←
(d) 25x  400
2
(e) 16x  25
2
1
Dammam Community College
MATH 011
5. The number of possible positive and the number of possible negative real zeros of the polynomial
P ( x)  5x4  12x3  6x2  3x 1 are
(a)
(b)
(c)
(d)
(e)
One positive and either three or one negative
One positive and three negative zeros
One positive and one negative
One negative and either three or one positive
One negative and three positive zeros
←
6. According to Descartes’ rule of signs, the polynomial P ( x)  4x4 12x3  3x2  12x  7 has
(a) One or three negative real zeros
(b)
(c)
(d)
(e)
One negative real zero ←
Four positive real zeros
No positive real zero
Three negative real zeros
7. If i   1 is a zero of the polynomial P( x)  x 4  2 x 3  2 x 2  2 x  1, then the number of the
x  intercepts of the graph of P (x ) is equal to
Answer:
1.
8. Let P be a polynomial function of x with leading coefficient 1. If P is with lowest degree and has
zeros 3 (of multiplicity 2), 1  i, and 1  i , then the coefficient of x 2 in P is equal to
Answer: 23
9. If i is a zero of f ( x)  x 4  x 3  5x 2  x  6 , then the sum of all its real zeros is:
Answer:
1
10. If 1  i is a zero of x 4  7 x 3  18 x 2  22 x  A then A is equal to
Answer:
12
2
Dammam Community College
MATH 011
11. A polynomial of lowest degree with only real coefficients having –2i, i, and 0 (multiplicity 2) as
zeros is
2
2
2
(a) x ( x  4)( x  1)
(b) x4  3x3  4 x2
(c) x 4  ix 3  2 x 2
(d) x 6  5x 4  4 x 2
(e) x  8x  4 x
6
4
←
2
12. The lowest degree of a polynomial with real coefficients having the zeros “3 of multiplicity 2, –5,
4+i, 7–i, and 7+i” is
(a)
(b)
(c)
(d)
(e)
7
6
5
8
9
←
13. A polynomial of lowest degree and real coefficients having 1 i and i as zeros is :
(a) x4  2 x3  3x2  2 x  2
(b)
(c)
(d)
(e)
←
x4  2 x3  3x2  2 x  2
x4  2 x3  3x2  2 x  2
x4  2 x3  3x2  2 x  2
x4  2 x3  3x2  2 x  2
14. If 1 i is a zero of the polynomial p( x)  x  2 x  3x  2 x  2 then the set of the remaining zeros
contains
4
(a)
(b)
(c)
(d)
(e)
3
2
Three non-real numbers ←
One non-real and two rational numbers
One non-real and two irrational numbers
Two non-real and one rational numbers
One rational and two irrational numbers
3