Extra Questions For Class 10 Maths Chapter 2 Polynomials

Extra Questions For Class 10 Maths Chapter 2 Polynomials

Here we are providing extra questions for class 10 maths chapter 2 polynomials. These questions are prepared by subject expert. Students can use these extra questions for practice.

QUADRATIC POLYNOMIAL
Relationship between zeroes and coefficients
General form of Quadratic polynomial: ax² + bx + c, a ≠ 0

Sum of zeroes (α + β) = -b/a; Product of zeroes (αβ) = c/a

Question: Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2, respectively.
Solution: Here, α + β = – 3 and αβ = 2
We know that quadratic polynomial is given by p(x) = x² – (α + β)x + αβ
= x² – (–3)x + 2 = x² + 3x + 2
Hence, required quadratic polynomial is x² + 3x + 2

Question: Find a quadratic polynomial, whose zeroes are – 3 and 2.
Solution: Here, α = – 3 and β = 2.
Now, α + β = – 3 + 2 = – 1 and αβ = (– 3)(2) = – 6
We know that quadratic polynomial is given by p(x) = x² – (α + β)x + αβ
= x² – (–1)x + (– 6) = x² + x – 6
Hence, required quadratic polynomial is x² + x – 6

Q.1. Find a quadratic polynomial, the sum and product of whose zeroes are – 5 and 3, respectively.

Q.2. Find a quadratic polynomial, whose zeroes are – 4 and 1, respectively.

Q.3. Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2, respectively. Also find its zeroes.

Q.4. 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.
(i) -8/3, 4/3
(ii) 21/8, 5/16
(iii) -2√3, -9
(iv) -3/2√5, -1/2

Q.5. Find the zeroes of the quadratic polynomial x² + 7x + 10, and verify the relationship between the
zeroes and the coefficients.

Q.6. Find the zeroes of the polynomial x² – 3 and verify the relationship between the zeroes and the
coefficients.

Q.7. Find the zeroes of the quadratic polynomial 6x² – 3 – 7x and verify the relationship between the
zeroes and the coefficients.

Q.8. Find the zeroes of the quadratic polynomial 3x² – x – 4 and verify the relationship between the
zeroes and the coefficients.

Q.9. Find the zeroes of the polynomial x²+x/6-2, and verify the relation between the coefficients and the zeroes of the polynomial.

Q.10. Find the zeroes of the quadratic polynomial 4x² – 4x + 1 and verify the relationship between the
zeroes and the coefficients.

Q.11. If α and β are the zeroes of the quadratic polynomial f(x) = x² – 3x – 2, then find a quadratic polynomial whose zeroes are 1/(2α+β) and 1/(2β+ α).

Q.12. If α and β are the zeroes of the quadratic polynomial f(x) = 2x² – 5x + 7, then find a quadratic
polynomial whose zeroes are 2 α + 3 β and 2 β + 3 α .

Q.13. If α and β are the zeroes of the quadratic polynomial f(x) = x² – 1, then find a quadratic
polynomial whose zeroes are 2α/β and 2β/α.

Q.14. If α and β are the zeroes of the quadratic polynomial f(x) = x² – 2x + 3, then find a quadratic
polynomial whose zeroes are α+2 and β+2.

Q.15. Obtain all other zeros of (x⁴ + 4x³ – 2x² – 20x – 15) if two of its zeros are √5 and – √5.

Ans. -1, -3

Q.16. If α and β are the zeroes of the quadratic polynomial f(x) = 2x² + 5x + k such that α²+β²+αβ=21/4, find the value of k.

Q.17. If 3 and –3 are two zeros of the polynomial (x⁴ + x³ – 11x² – 9x + 18), find all the zeros of the given polynomial.

Ans. 1, -2, 3, -3

Q.18. Find all the zeros of the polynomial (2x⁴ – 11x³ + 7x² + 13x – 7), it being given that two of its zeros are (3 + √2) and (3 – √2).

Ans. (3+√2), (3-√2), 1/2, -1

Q.19. If 2 and –2 are two zeros of the polynomial (x⁴ + x³ – 34x² – 4x + 120), find all the zeros of the given polynomial.

Ans. 2, -2, -6, 5

Q.20. Find all the zeros of (x⁴ + x³ – 23x² – 3x + 60), if it is given that two of its zeros are √3 and – √3.

Ans. √3, – √3, 4, -5

Q.21. If 1 and –2 are two zeros of the polynomial (x³ – 4x² – 7x + 10), find its third zero.

Ans. 13

Q.22. Find all the zeros of (2x⁴ – 3x³ – 5x² + 9x – 3), it being given that two of its zeros are √3 and – √3.

Ans. √3, –√3, 1, 1/2

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