Different types of question from polynomial class 10.
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Step-by-step explanation:
Find the zeroes of quadratic polynomial and verify the relationship between the zeros and coefficients
second question find all the zeros of two of its zeros are given
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1. Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficient of the polynomial.
2. Find the zeroes of the quadratic polynomial 5x2 – 4 – 8x and verify the relationship between the zeroes and the coefficient of the polynomial.
3. Find the quadratic polynomial, the sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
4. If one zero of the polynomial (a2 – 9) x2 + 13x + 6a is reciprocal of the other, find the value of ‘a'
5. If the product of zeroes of the polynomial ax2 – 6x – 6 is 4, find the value of ‘a’.
6. Find all the zeros of the polynomial x4 + x3 – 34x2 – 4x + 120, if two of its zeroes are 2 and – 2.
7. Find all the zeroes of the polynomial 2x4 + 7x – 19x2 – 14x + 30, if two of its zeroes are 
8. Find the quadratic polynomial whose zeroes are 1 and –3. Verify the relation between the coefficients and the zeroes of the polynomial.
9. Find the zeroes of the quadratic polynomial 4x2 – 4x – 3 and verify the relation between the zeroes and its coefficients.
10. Obtain all other zeroes of the polynomial 2x3 – 4x – x2 + 2, if two of its zeroes are 
11. Find all the zeroes of x4 – 3x3 + 6x – 4, if two of its zeroes are 
12. Find a quadratic polynomial whose zeroes are –4 and 3 and verify the relationship between the zeroes and the coefficients.
13. Using division algorithm, find the quotient and remainder on dividing f(x) by g(x), where f(x) = 6x3 + 13x2 + x – 2 and g(x) = 2x + 1
14. If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another polynomial 3x2 + 4x + 1 then the remainder comes out to be ax + b, find ‘a’ and ‘b’
15. If the polynomial x4 + 2x3 + 8x2 + 12x + 18 is divided by another polynomial x2 + 5, the remainder comes out to be px + q. Find the value of p and q.
16. Find all the zeroes of the polynomial x3 + 3x2 – 2x – 6, if two of its zeroes
28. Find all the zeroes of the polynomial 2x3 + x2 – 6x – 3, if two of its zeroes are – 
29. If α and β are zeroes of the quadratic polynomial x2 – 6x + a; find the value of ‘a’ if 3α + 2β = 20.
2. Find the zeroes of the quadratic polynomial 5x2 – 4 – 8x and verify the relationship between the zeroes and the coefficient of the polynomial.
3. Find the quadratic polynomial, the sum of whose zeroes is 8 and their product is 12. Hence, find the zeroes of the polynomial.
4. If one zero of the polynomial (a2 – 9) x2 + 13x + 6a is reciprocal of the other, find the value of ‘a'
5. If the product of zeroes of the polynomial ax2 – 6x – 6 is 4, find the value of ‘a’.
6. Find all the zeros of the polynomial x4 + x3 – 34x2 – 4x + 120, if two of its zeroes are 2 and – 2.
7. Find all the zeroes of the polynomial 2x4 + 7x – 19x2 – 14x + 30, if two of its zeroes are 
8. Find the quadratic polynomial whose zeroes are 1 and –3. Verify the relation between the coefficients and the zeroes of the polynomial.
9. Find the zeroes of the quadratic polynomial 4x2 – 4x – 3 and verify the relation between the zeroes and its coefficients.
10. Obtain all other zeroes of the polynomial 2x3 – 4x – x2 + 2, if two of its zeroes are 
11. Find all the zeroes of x4 – 3x3 + 6x – 4, if two of its zeroes are 
12. Find a quadratic polynomial whose zeroes are –4 and 3 and verify the relationship between the zeroes and the coefficients.
13. Using division algorithm, find the quotient and remainder on dividing f(x) by g(x), where f(x) = 6x3 + 13x2 + x – 2 and g(x) = 2x + 1
14. If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another polynomial 3x2 + 4x + 1 then the remainder comes out to be ax + b, find ‘a’ and ‘b’
15. If the polynomial x4 + 2x3 + 8x2 + 12x + 18 is divided by another polynomial x2 + 5, the remainder comes out to be px + q. Find the value of p and q.
16. Find all the zeroes of the polynomial x3 + 3x2 – 2x – 6, if two of its zeroes
28. Find all the zeroes of the polynomial 2x3 + x2 – 6x – 3, if two of its zeroes are – 
29. If α and β are zeroes of the quadratic polynomial x2 – 6x + a; find the value of ‘a’ if 3α + 2β = 20.
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