Polynomials Class 10 Extra Questions with Answers

Polynomials Class 10 Extra Questions

MULTIPLE CHOICE QUESTIONS

1. The number of polynomials having -2 and 5 as zeroes is a) Exactly 1                     b) only 2                      c) atmost 2      d) infinitely many.
2. If one zero of the polynomial x² – 3kx +4k be twice the other, then the value of k is a) 2                      b) – 2               c) ½                 d) -1/2
3. If 𝛼 𝑎𝑛𝑑 𝛽 are the zeroes of the polynomial ax² – 5x + c and  𝛼 + 𝛽 = 𝛼 𝛽 = 10, then: a) a = 5, c = ½     b) a = 1, c = 5/2           c) a = 5/2, c = 1           d) a = ½, c = 5
4. If one zero of the polynomial 6x² + 37x – (k-2) is reciprocal of the other, then what is the value of k? a) – 4                   b) 6                  c) – 6               d) 4
5. If 𝛼 𝑎𝑛𝑑 𝛽 are the zeroes of the polynomial f (x) = x² + x – 1, then a) 1                      b) – 1               c) 0                  d) none of these
6. A quadratic polynomial, the sum of whose zeroes is 0 and one zero is 3,is a) x² – 9               b) x² + 9          c) x² + 3           d) x² – 3
7. If  𝛼 𝑎𝑛𝑑 𝛽 are the zeroes of the quadratic polynomial p(x) = x² – ax –b, then the value of  𝛼² + 𝛽² is a) a² – 2b                        b) a² + 2b                   c) b² – 2a                    d) b² + 2a
8. The zeroes of the polynomial x² – 3x – m(m+3) are a) m, m+3           b) – m, m + 3             c) m, -(m+3)             d) –m, – (m+3) Polynomials Class 10 Extra Questions SUBJECTIVE TYPE QUESTIONS
9. If the quadratic polynomial ax²+bx +c has 2 same zeroes with opposite signs then what is the value of b?
10. If one zero of a quadratic polynomial ax²+bx +c is zero then what is the value of c?
11. What constant should be added to polynomial x²+7x+5 so that -2 is a zero of the resulting polynomial?
12. Find the zeroes of the quadratic polynomial x² + 7x + 12 and verify the relation between the zeroes and coefficients.
13. If 2 and ½ are zeroes of px² + 5x + r, then find the values of p and r
14. If a and b are the zeroes of the quadratic polynomial f(x) = x²– x – 2, find a polynomial whose zeroes are 2a+1 and 2b+1.
15. If a and b are the zeroes of the quadratic polynomial f(x) = 3x²-4x+1, find a quadratic polynomial whose zeroes are a²/b and b²/a
16. Find the value of k such that the polynomial x² – (k+6) x +2(2k-1) has sum of its zeroes equal to half their product.
17. If 𝛼 𝑎𝑛𝑑 𝛽 are the zeroes of the quadratic polynomial f(x) = x² – 4x +3, find the value of  (𝛼⁴𝛽² +𝛼² 𝛽⁴)
18. If a and b are the zeroes of the quadratic polynomial such that a+b =24 and a-b = 8, find a quadratic polynomial having a and b as its zeroes.
19. If α and β are the zeroes of the polynomial f(x) = 2 x² + 5 x + k satisfying the relation 𝛼²+𝛽²+𝛼 𝛽 = 21/4. Find the values of k for this to be possible.
20. If one of the zeroes of the quadratic polynomial f (x) = 14x² – 42 k²x – 9 is negative of the other, find the value of k.
21. The graph of y=p(x) is given in the adjoining figure. Zeros of the polynomial p(x) are
22. If α and β are the zeroes of the polynomial f(x) = kx² + 4 x + 4 satisfying the relation α² + β²  = 24. Find the values of k.
23. If α and β are the zeroes of the polynomial f(x) = x² – 5x + k such that α- β = 1. Find the value of k.
24. Find the zeroes of the polynomial: .
25. Find a quadratic polynomial with zeroes 3 +  and 3 – .
26. If α and β are the zeroes of the polynomial f(x) = 4x² – 2 x + (k – 4) and α = .Find the values of k.
27. If α and β are the zeroes of the polynomial f(x) = x² – 4x + 3, then form a quadratic polynomial whose zeroes are 3 α + 2  and 3β + 2
28. If α and β are the two zeroes of the polynomials 25 p² – 15 p + 2, find a quadratic polynomial whose zeroes are 1/2α and 1/2β.
29. If sum of the squares of zeros of the quadratic polynomial x²– 8x +k is 40, find the value of k.
30. If the sum of the zeros of the quadratic polynomial kt²+ 2t +3k is equal to their product, find the value of k.
31. If the squared difference of the zeros of the quadratic polynomial x²+ px +45 is equal to 144, find the value of p.
32. If α and β are the zeros of quadratic polynomial x²– p(x+1)-c, show that (α+1) ( β+1)=1-c. 
33. If α and β are the zeroes of the quadratic polynomial f(x) = x² + x – 2, find the value of  1/α – 1/β.
34. Assertion (A): If the zeroes of the quadratic polynomial (k – 1) x² + kx + 1 is – 3, then value of k is 4/3. Reason (R): If -1 is a zero of the polynomial p(x) = kx² – 4x + k, then the value of k is – 2.
35. Assertion (A): If both zeroes of the quadratic polynomial x² – 2kx +2 are equal in magnitude but opposite in sign then value of k is ½ Reason (R): Sum of zeroes of a quadratic polynomial ax² + bx + c is –b/a.
36. Assertion (A): The polynomial P(x) = x² + 3x +3 has 2 real zeroes. Reason (R): A quadratic polynomial can have at most two real Click below for CBSE CLASS 10 MATHS EXTRA QUESTIONS WITH SOLUTIONS https://sharmatutorial.in/important-questions-class-10-maths-with-solutions-pdf/

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Polynomials Class 10 Extra Questions

Polynomials Class 10 Extra Questions