Polynomials Worksheet-1

    ~Anshul Gurjar

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Other Important MCQ's with Answers

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