Theory of Equations - Choose the correct Answers | 12th Mathematics : UNIT 3 : Theory of Equations
Chapter: 12th Mathematics : UNIT 3 : Theory of Equations
Choose the correct Answers
Choose the correct or the most suitable answer from the given four alternatives :
1. A zero of x3 + 64 is
(1) 0
(2) 4
(3) 4i
(4) -4
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
(1) mn
(2) m + n
(3) mn
(4) nm
3. A polynomial equation in x of degree n always has
(1) n distinct roots
(2) n real roots
(3) n imaginary roots
(4) at most one root.
4. If α , β , and γ are the zeros of x3 + px2 + qx + r , then 
is
(1) -q/r
(2) -p/r
(3) q/r
(4) -q/p
5. According to the rational root theorem, which number is not possible rational zero of 4x7 + 2x4 −10x3 − 5 ?
(1) −1
(2) 5/4
(3) 4/5
(4) 5
6. The polynomial x3 − kx2 + 9x has three real zeros if and only if, k satisfies
(1) |k| ≤ 6
(2) k = 0
(3) |k| > 6
(4) |k| ≥ 6
7. The number of real numbers in [0, 2π] satisfying sin4 x − 2 sin2 x +1 is
(1) 2
(2) 4
(3) 1
(4) ∞
8. If x3 +12x2 +10ax +1999 definitely has a positive zero, if and only if
(1) a ≥ 0
(2) a > 0
(3) a < 0
(4) a ≤ 0
9. The polynomial x3 + 2x + 3 has
(1) one negative and two imaginary zeros
(2) one positive and two imaginary zeros
(3) three real zeros
(4) no zeros
10. The number of positive zeros of the polynomial 
is
(1) 0
(2) n
(3) < n
(4) r
Choose the correct or the most suitable answer from the given four alternatives :
1. A zero of x3 + 64 is
(1) 0
(2) 4
(3) 4i
(4) -4
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
(1) mn
(2) m + n
(3) mn
(4) nm
3. A polynomial equation in x of degree n always has
(1) n distinct roots
(2) n real roots
(3) n imaginary roots
(4) at most one root.
4. If α , β , and γ are the zeros of x3 + px2 + qx + r , then is
(1) -q/r
(2) -p/r
(3) q/r
(4) -q/p
5. According to the rational root theorem, which number is not possible rational zero of 4x7 + 2x4 −10x3 − 5 ?
(1) −1
(2) 5/4
(3) 4/5
(4) 5
6. The polynomial x3 − kx2 + 9x has three real zeros if and only if, k satisfies
(1) |k| ≤ 6
(2) k = 0
(3) |k| > 6
(4) |k| ≥ 6
7. The number of real numbers in [0, 2π] satisfying sin4 x − 2 sin2 x +1 is
(1) 2
(2) 4
(3) 1
(4) ∞
8. If x3 +12x2 +10ax +1999 definitely has a positive zero, if and only if
(1) a ≥ 0
(2) a > 0
(3) a < 0
(4) a ≤ 0
9. The polynomial x3 + 2x + 3 has
(1) one negative and two imaginary zeros
(2) one positive and two imaginary zeros
(3) three real zeros
(4) no zeros
10. The number of positive zeros of the polynomial is
(1) 0
(2) n
(3) < n
(4) r
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