**Assertion and Reason Questions for Class 10 Maths Chapter 2 Polynomials**

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

(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).

(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).

(C) Assertion (A) is true but reason (R) is false.

(d) Assertion (A) is false but reason (R) is true.

**Q.1. Assertion:** x^{2}+7x+12 has no real zeroes. **Reason: **A quadratic polynomial can have at the most two zeroes.

## Answer

Answer: (d)**Q.2. Assertion:** If the sum of the zeroes of the quadratic polynomial x^{2}-2kx+8 is 2 then value of k is 1. **Reason: **Sum of zeroes of a quadratic polynomial ax^{2}+bx+c is -b/a

## Answer

Answer: (a)**Q.3. Assertion: **P(x) = 4x^{3}-x^{2}+5x^{4}+3x-2 is a polynomial of degree 3. **Reason: **The highest power of x in the polynomial P(x) is the degree of the polynomial.

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Answer: (d)**Q.4. Assertion:** x^{3}+x has only one real zero. **Reason: **A polynomial of nth degree must have n real zeroes.

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Answer: (c)**Q.5. Assertion:** If one zero of polynomial p(x) = (k^{2}+4)x^{2}+13x+4k is reciprocal of the other, then k=2. **Reason:** If (x-a) is a factor of p(x), then p(a) = 0 i.e., a is a zero of p(x).

## Answer

Answer: (b)**Q.6. Assertion: **x^{2}+4x+5 has two zeroes. **Reason:** A quadratic polynomial can have at the most two zeroes.

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Answer: (d)**Q.7. Assertion: **Degree of aa zero polynomial is not defined. **Reason:** Degree of a non-zero constant polynomial is 0.

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Answer: (b)**Q.8. Assertion:** If the product of the zeroes of the quadratic polynomial x^{2}+3x+5k is -10 then value of k is -2. **Reason: **Sum of zeroes of a quadratic polynomial ax^{2}+bx+c is -b/a

## Answer

Answer: (b)**Q.9. Assertion: **The graph y=f(x) is shown in figure, for the polynomial f(x). The number of zeroes of f(x) is 3. **Reason: **The number of zero of the polynomial f(x) is the number of point of which f(x) cuts or touches the axes.

## Answer

Answer: (c)**Q.10. Assertion:** 3-2√5 is one zero of the quadratic polynomial then other zero will be 3+2√5. **Reason:** Irrational zeros (roots) always occurs in pairs.

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Answer: (a)**Q.11. Assertion:** (2 − √3) is one zero of the quadratic polynomial then other zero will be (2 + √3) .**Reason:** Irrational zeroes (roots) always occurs in pairs.

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Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).**Q.12. Assertion:** If one zero of polynomial p(x) = (k + 4) x^{2} + 13x + 3k 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).

## Answer

Answer: (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).**Q.13. Assertion:** A polynomial of degree 5 is divided by a quadratic polynomial. If it leaves a remainder, then the degree of remainder is 1 or 0. **Reason:** Degree of remainder is always less than divisor.

## Answer

Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).**Q.14. Assertion:** The polynomial p(x) = 5x – 1/2 is a linear polynomial. **Reason:** The general form of linear polynomial is ax+b.

## Answer

Answer: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).**Q.15. Assertion:** The graph of a polynomial intersect x-axis at 3 points and y-axis at 1 points, the polynomial has 3 zeroes. **Reason: **The number of zeroes that a polynomial p(x) can have is the number of times polynomial intersect x and y axis.

## Answer

Answer: (c) Assertion is correct but reason is wrong.**Frequently Asked Questions (FAQs)**

**What is an algebraic expression?**

An algebraic expression consists of variables, constants and mathematical operators.

**What is a polynomial?**

Polynomial is an algebraic expression in which the exponent on any variable is a whole number.

**How to find the degree of polynomial from an algebraic expression?**

Highest power of x in the given algebraic expression.

**How many types of polynomials are there on the basis of number of terms?**

There are three types- monomial, binomial and trinomial.

**How many types of polynomials are there on the basis of degree of polynomial?**

There are three types- Linear, Quadratic and Cubic polynomials.

**What is zero of a polynomial?**

A zero of a polynomial p(x) is the value of x for which the value of the polynomial p(x) is 0.

**How many zeros can a linear polynomial have?**

One zero

**How many zeros can a quadratic polynomial have?**

At most two zeros.

In given question 6 the answer is totally wrong same with question 5. It is given Assertion: x2+4x+5 has two zeroes.

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

In which both are true and r us correct explanation of a but idk from what logic the answer is given as d when it should be a.

I would like the owner or the it team of this website to change it. It creates alot of confusion when looking into the answers.

A quadratic polynomial can have maximum 2 zeroes. But it can have one zero also. For example, x2-4x+4=0 has one distinct zero -2. You can visualize graphically too. A quadratic polynomial can touch the x axis at one point also. So in that case it will have one zero not zero. But it is true that it will never have more than one zero. I hope, it helps.

Answer of question 6 is completely wrong.

We know that,

D=b²-4ac

D= -4

So, as the D is negative,

The roots will be imaginary and hence there will be no real roots!

Given answer is correct.

Yes but the question said zeros and did not specify that the zeros are reals so the answer should be (a)