Polynomials Worksheet-1
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Below are the MCQs of Chapter 2-Polynomials
1.The dimensions of x2-2x -8 are:
(a) (2, -4)
(b) (4, -2)
(c) (- 2, -2)
(d) (- 4, -4)
Answer: (b)
Description: x2-22x -8 = x2-4x + 2x -8
= x (x-4) +2 (x-4)
= (x-4) (x + 2)
Therefore, x = 4, 2.
2. What is the quadratic polynomial of its sum and the product of zeroes √2, ⅓ respectively?
(a) 3x2-3√2x + 1
(b) 3x2 + 3√2x + 1
(c) 3x2 + 3√2x-1
(d) None of the above
Answer: (a)
Definition: The sum of zeroes = α + β = √2
Product of zeroes = α β = 1/3
∴ If α and β are the dimensions of any quadratic polynomial, then the polynomial is;
x2– (α + β) x + αβ
= x2 - (√2) x + (1/3)
= 3x2-3√2x + 1
3. If the zeroes of quadratic polynomial ax2 + bx + c, c ≠ 0 are equal, then
(a) c and b have different characteristics
(b) c and have distinctive marks
(c) c and b have similar symptoms
(d) c and have similar signs
Answer: (d)
Description:
At the root of equality, prejudice will be equal to zero.
b2 -4ac = 0
b2 = 4ac
ac = b2 / 4
ac> 0 (square of any number cannot be negative)
4. The polynomial level, x4 - x2 +2 is
(a) 2
(b) 4
(c) 1
(d) 0
Answer: b
Definition: Degree the greatest potential for variability in any polynomial.
5. If one of the cubic polynomial sizes is x3 + ax2 + bx + c is -1, then the product of two other dimensions:
(a) b-a-1
(b) b-a +1
(c) a-b + 1
(d) a-b-1
Answer: (b)
Definition: Since one zero is -1, hence;
P of (x) = x3 + ax2 + bx + c
P (-1) = (-1) 3 + a (-1) 2 + b (-1) + c
0 = -1 + a-b + c
c = 1-a + b
Product of zero, αβγ = -constant term / coeff is x3
(-1) βγ = -c / 1
c = βγ
βγ = b-a + 1
6. If p (x) is a polynomial of one degree and p (a) = 0, then it is called:
(a) Zero p (x)
(b) P value (x)
(c) General of p (x)
(d) None of the above
Answer: (a)
Definition: Let p (x) = mx + n
Put x = a
p (a) = ma + n = 0
Therefore, zero is p (x).
7. Zeroes of a polynomial can be highlighted. The number of polynomial sizes is equal to the number of points on which the polynomial graph is:
(a) Suggest an x-axis
(b) The distance between y-axis
(c) Axis or x-axis level
(d) None of the above
Answer: (a)
8. Polynomial degree n contains:
(a) Only one zero
(b) At least y zeroes
(c) Above zero
(d) At least zero
Answer: (d)
Definition: Maximum number of polynomial sizes = Degree of polynomial
9. The number of polynomials with zeroes like 2 and 5 is:
(a) 1
(b) 2
(c) 3
(d) More than 3
Answer: (d)
Description: Polynomials x2-3x-10, 2x2-6x-20, (1/2) x2- (3/2) x-5, 3x2-9x-30, with zeros as 2 and 5.
10. Zeroes of p (x) = x2-27 are:
(a) ± 9√3
(b) ± 3√3
(c) ± 7√3
(d) None of the above
Answer: b
Description: x2-27 = 0
x2 = 27
x = √27
x = ± 3√3
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