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Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 1

Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

**Assertion :** The sum and product of the zeros of a quadratic polynomial are respectively.

Then the quadratic polynomial is 4x^{2} +x+1.

**Reason : **The quadratic polynomial whose sum and product of zeros are given is x^{2}-(sum of zeros). x + product of zeros.

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 1

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 2

Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

**Assertion :** If (x + 1) is a factor of f(x) = x^{2} + ax + 2, then a = - 3.

**Reason : **If (x - a) is a factor of p (x), if p (a) = 0.

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 2

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 3

Direction: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:

**Assertion : **If both zeros of the quadratic polynomial x^{2} - 2kx + 2 are equal in magnitude but opposite in sign then value of k is 1/2.

**Reason : **Sum of zeros of a quadratic polynomial ax^{2} + bx + c is b/a

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 3

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 4

**Assertion :** x^{3} + x has only one real zero.

**Reason : **A polynomial of nth degree must have n real zeroes.

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 4

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 5

**Assertion : **The remainder when p(x) = x^{3} - 6x^{2} + 2x - 4 is divided by (3x - 1) is -107/27.

**Reason : **If a polynomial p(x) is divided by ax - b , the remainder is the value of p(x) at x = b/a.

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 5

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 6

**Assertion : **P(x) = 14x^{3} - 2x^{2} + 8x^{4} + 7x - 8 is a polynomial of degree 3.

**Reason : **The highest power of x in the polynomial p(x) is the degree of the polynomial.

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 6

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 7

**Assertion :** (x + 2) is a factor of x^{3} + 3x^{2} + 5x + 6 and of 2x + 4.

**Reason : **If p(x) be a polynomial of degree greater than or equal to one, then (x - a) is a factor of p(x), if p(a) = 0

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 7

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 8

**Assertion :** If one zero of poly-nominal p(x) = (k^{2} + 4)x^{2 }+ 13x + 4k is reciprocal of other, then k = 2.

**Reason : **If (x - α) is a factor of p(x), then p(α) = 0

i.e. α is a zero of p(x).

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 8

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 9

**Assertion : **The expression 3x^{4} - 4x^{3/2} + x^{2} = 2 is not a polynomial because the term -4x^{3/2} contains a rational power of x.

**Reason : **The highest exponent in various terms of an algebraic expression in one variable is called its degree.

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 9

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 10

**Assertion : **x^{2} + 4x + 5 has two zeroes.

**Reason : **A quadratic polynomial can have at the most two zeroes.

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 10

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 11

**Assertion : **3x^{2} + x - 1 = (x + 1) (3x - 2) + 1.

**Reason : **If p(x) and g(x) are two polynomials such that degree of p(x) ≥ degree of g(x) and g(x) ≥ 0 then we can find polynomials q(x) and r(x) such that p(x) = g(x) q(x) + r (x), where r(x) = 0 of degree of r(x) < degree of g(x).

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 11

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 12

**Assertion : **Zeroes of f(x) = x^{2} - 4x - 5 are 5, - 1

**Reason : **The polynomial whose zeroes are 2 + √3, 2 - √3 is x^{2} - 4x + 7.

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 12

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 13

**Assertion :** (x + 2) and (x - 1) are factors of the polynomial x^{4} + x^{3} + 2x^{2} + 4x - 8.

**Reason : **For a polynomial p(x) of degree ≥ 1, x - a is a factor of the polynomial p(x) if and only if p(a) ≥ 1.

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 13

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 14

**Assertion : **(2 - √3) is one zero of the quadratic polynomial then other zero will be (2 + √3).

**Reason : **Irrational zeros (roots) always occurs in pairs.

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 14

Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 15

**Assertion : **If f(x) = 3x^{7} - 4x^{6} + x + 9 is a polynomial, then its degree is 7.

**Reason :** Degree of a polynomial is the highest power of the variable in it.

Detailed Solution for Test: Polynomials- Assertion & Reason Type Questions- 2 - Question 15

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