Here you get the CBSE Class 10 Mathematics chapter 2, Polynomials: NCERT Exemplar Problems and Solutions (Part-III). This part of the chapter includes solutions for Exercise 2.4 of NCERT Exemplar Problems for Class 10 Mathematics Chapter: Polynomials. This exercise comprises of only the Long Answer Type Questions framed from various important topics in the chapter. Each question is provided with a detailed solution.

**NCERT Exemplar Solution for CBSE Class 10 Mathematics Chapter: Polynomials (Part-I)**

NCERT Exemplar problems are a very good resource for preparing the critical questions like Higher Order Thinking Skill (HOTS) questions. All these questions are very important to prepare for CBSE Class 10 Mathematics Board Examination 2017-2018 as well as other competitive exams.

**NCERT Exemplar Solution for CBSE Class 10 Mathematics Chapter: Polynomials (Part-II)**

**Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Polynomials:**

**Exercise 2.4**

** Long Answer Type Questions**

**Q. 1** For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also, find the zeroes of these polynomials by factorisation.

**NCERT Exemplar Solution for CBSE Class 10 Mathematics Chapter: Polynomials (Part-III)**

**Main concept for solving the above questions is:**

- If
*α*and*β*are the two zeroes of a polynomial then that polynomial can be expressed as:

*f *(*x*) = *x*^{2 }– (*α* + *β*)*x* + *αβ*

Or *f *(*x*) = *x*^{2 }– (Sum of roots, S)*x *+ (Product of roots, P)

- Then the quadratic polynomial so formed will be factorised by splitting the middle term to obtain the required zeroes.

**Q. 2 **If the zeroes of the cubic polynomial *x*^{3} – 6*x*^{2} + 3*x* +10 are of the form *a*, *a* + *b* and *a* + 2*b* for some real number *a* and *b*, find the values of *a* and *b* as well as the zeroes of the given polynomial.

**Solution. **

**Q. 4 **Find *k* so that *x*^{2} + 2*x* + *k* is a factor of 2*x*^{4} + *x*^{3} – 14*x*^{2} + 5*x* + 6. Also, find all the zeroes of the two polynomials.

**Solution. **

**Q. 6 **For which values of* a* and *b*, the zeroes of *q*(*x*) = *x*^{3} + 2*x*^{2} + *a *are also the zeroes of the polynomial *p*(*x*) = *x*^{5 }− *x*^{4 }− 4*x*^{3} + 3*x*^{2} + 3*x* + *b*. Which zeroes of *p*(*x*) are not the zeroes of *q*(*x*)?

**Solution.**

Given that zeroes of *q*(*x*) = *x*^{3} + 2*x*^{2} + *a* are also the zeroes of the polynomial *p*(*x*) = *x*^{5 }− *x*^{4 }− 4*x*^{3} + 3*x*^{2} + 3*x* + *b*, it means *q*(*x*) is a factor of* p*(*x*) .

By using division algorithm,

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