# Topic: Chapter 3: Theory of Equations (Test 1)

Topic: Chapter 3: Theory of Equations
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• Test: 1(current)
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Q.1
A zero of x3 + 64 is
A. 0
B. 4
C. 4i
D. -4
Explaination / Solution: Workspace
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Q.2
If f and g are polynomials of degrees m and n respectively, and if h(x) = ( f o g )(x) , then the degree of h is
A. mn
B. m + n
C. mn
D. nm
Explaination / Solution: Workspace
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Q.3
A polynomial equation in x of degree n always has
A. n distinct roots
B. n real roots
C. n imaginary roots
D. at most one root.
Explaination / Solution:

A polynomial of degree n always has n roots
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Q.4
If α , β , and  γ  are the zeros of  x+ px+ qx + r , then is
A. -q/r
B. -p/r
C. q/r
D. -q/p
Explaination / Solution: Workspace
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Q.5
According to the rational root theorem, which number is not possible rational zero of 4x+ 2x4 10x3 5 ?
A. −1
B. 5/4
C. 4/5
D. 5
Explaination / Solution: Workspace
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Q.6
The polynomial x3 kx2 + 9x has three real zeros if and only if, k satisfies
A. |k| ≤ 6
B. k = 0
C. |k| > 6
D. |k| ≥ 6
Explaination / Solution: Workspace
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Q.7
The number of real numbers in [0, 2π] satisfying sin4 x 2 sin2 x +1 is
A. 2
B. 4
C. 1
D.
Explaination / Solution: Workspace
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Q.8
If x3 +12x2 +10ax +1999 definitely has a positive zero, if and only if
A. a ≥ 0
B. a > 0
C. a < 0
D. a ≤ 0
Explaination / Solution: Workspace
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Q.9
The polynomial x3 + 2x + 3 has
A. one negative and two imaginary zeros
B. one positive and two imaginary zeros
C. three real zeros
D. no zeros
Explaination / Solution: Workspace
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Q.10
The number of positive zeros of the polynomial is
A. 0
B. n
C. < n
D. r 