The document Worksheet Questions - Polynomials Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.

All you need of Class 10 at this link: Class 10

**Test Your Skills****1. **Find the quadratic polynomial whose zeroes arerespectively.**2.** Find the zeroes of the polynomial â€“ 2.**3. **Divide: x^{3} âˆ’ 1 by x + 1.**4.** Find the quadratic polynomial whose zeroes are respectively.**5.** Divide: x^{4} âˆ’ 1 by x + 1.**6.** Divide: 4x^{3} âˆ’ x + 1 by 2x âˆ’ 1.**7.** Divide: x^{4} + x^{2} + 1 by x^{2} + x + 1.**8.** Find the quotient and remainder when x^{4} + 1 is divided by x âˆ’ 1.**9.** Find the quotient and remainder when f (x) = 4x^{3} âˆ’ 12x^{2} + 14x âˆ’ 13 is divided by **10.** Find the quotient and remainder when 3x^{4} + 5x^{3} â€“7x^{2} + 2x + 2 is divided by x^{2} + 3x + 1.**11**. Find the remainder when x^{4} â€“ 3x^{2} + 4x + 5 is divided by x^{2} â€“ x + 1.**12.** On dividing x^{3} âˆ’ 3x^{2} + x + 2 by a polynomial g (x), the quotient and remainder were x âˆ’ 2 and âˆ’ 2x + 4 respectively. Find g (x).**13.** Find the zeroes of 2x^{4} âˆ’ 3x^{3} âˆ’ 3x^{2} + 6x âˆ’ 2, if you know that two of its zeroes are âˆš2 and -âˆš2.**14.** If Î± and Î² are the zeroes of the quadratic polynomial f (x) = x^{2} âˆ’ 3x + 2, then find the value of Î±^{2} + Î²^{2}.**15.** It being given that 1 is one of the zeroes of the polynomial 7x âˆ’ x^{3} âˆ’ 6. Find its other zeroes.**Hint**: (âˆ’ x^{3} + 7x âˆ’ 6) Ã· (x âˆ’ 1)= âˆ’ (x^{2} + x âˆ’ 6) = âˆ’ [(x + 3) (x - 2)]

âˆ´ The other zeroes are âˆ’3 and 2.**16.** Divide 2x^{4} âˆ’ 9x^{3} + 5x^{2} + 3x âˆ’ 8 by x^{2} âˆ’ 4x + 1 and verify the division by algorithm.**Hint:** (2x^{4} âˆ’ 9x^{3} + 5x^{2} + 3x âˆ’ 8) Ã· (x^{2} âˆ’ 4x + 1)

â‡’ quotient = 2x^{2} âˆ’ x âˆ’ 1 and remainder = âˆ’7**Verification: **

(Quotient Ã— Divisor) + Remainder = Dividend or (2x^{2} âˆ’ x âˆ’ 1) Ã— (x^{2} âˆ’ 4x + 1) + (âˆ’ 7) = 2x^{4} âˆ’ 9x^{3} + 5x^{2} + 3x âˆ’ 8**17.** Find k so that x^{2} + 2x + k is a factor of 2x^{4}+ x^{3} â€“ 14x^{2} + 5x + 6. Also, find all the zeroes of the polynomial.**Hint:** For (x^{2} + 2x + k) to be a factor the remainder in (2x^{4} + x^{3} â€“ 14x^{2} + 5x + 6) Ã· (x^{2} + 2x + k) must be zero.**18.** If Î±, Î² are the zeroes of the quadraticpolynomial p(x) = x^{2} â€“ (kâ€“6)x + (2k + 1), find the value of k when Î± + Î² = Î±Î².**Hint:** Sum of roots Î± + Î² = â€“[â€“(k â€“ 6)]= k â€“ 6

Product of roots Î±Î² = 2k + 1

âˆµ Î± + Î² = Î±Î²

âˆ´ k â€“ 6 = 2k + 1

â‡’ (2kâ€“ k) = â€“ 6 â€“ 1

âˆ´ k = â€“7**19.** Find the zeroes of the polynomial p(x) = and verify the relationship between the zeroes and the coefficients.**Hint:**

In the given polynomial,

Product of roots

From (1), (2) and (3), the relation between the zeroes and coefficient is verified.**ANSWERS****1. **x^{2} â€“ 10x + 7**2. ****3.** x^{2} â€“ x + 1; Remainder = â€“2**4**. x^{2} â€“ 10x + 21**5.** x^{3} + x^{2} + x + 1; Remainder = â€“ 2**6. **2x^{2} + x; Remainder = 1**7. **x^{2} â€“ x + 1; Remainder = 0**8. **x^{3} + x^{2} + x + 1; Remainder = 2**9. **4x^{2} â€“ 10x + 19, Remainder = -7/2**10.** 3x^{2} â€“ 4x + 2; Remainder = 0**11.** Quotient = x^{2} + x â€“3; Remainder = 8**12.** g(x) = x^{2} â€“ x + 1**13.****14.** 5**15. **â€“3 and 2**16.** 2x^{2} â€“ x â€“ 1; Remainder = â€“ 7**17.** k = â€“ 3; zeroes; **18. **k = â€“7,**19.**

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

178 videos|268 docs|103 tests

### Value Based Questions - Polynomials

- Doc | 1 pages
### Facts That Matter- Polynomials

- Doc | 3 pages
### MCQ : Polynomials - 2

- Test | 15 ques | 20 min
### Previous Year Questions - Polynomials

- Doc | 2 pages
### Important definitions and formulas - Polynomials

- Doc | 1 pages

- MCQ : Polynomials - 1
- Test | 10 ques | 10 min
- Short Answer Type Questions (Part - 1) - Polynomials
- Doc | 9 pages