1. Find the condition that zeroes of polynomial p(x) = ax2 + bx + c are reciprocal of each other.
2. Form a quadratic polynomial whose zeroes are 3 + √2 and 3 – √2.
3. Find a quadratic polynomial, the sum and product of whose zeroes are √3 and 1√3 respectively.
4. Find a quadratic polynomial, the sum and product of whose zeroes are 0 and -√2 respectively.
5. Find the zeroes of the quadratic polynomial √3 x2 – 8x + 4√3.
6. If the zeroes of the polynomial x2 + px + q are double in value to the zeroes of 2x2 – 5x – 3, find the value of p and q.
7. Can (x – 2) be the remainder on division of a polynomial p(x) by (2x + 3)? Justify your answer.
8. Find a quadratic polynomial whose zeroes are 3+√55 and 3−√55.
9. Find the quadratic polynomial whose zeroes are -2 and -5. Verify the relationship between zeroes and coefficients of the polynomial.
10. Find the zeroes of the quadratic polynomial 3x2 – 75 and verify the relationship between the zeroes and the coefficients

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