Polynomial DPP 2

1. If the sum of zeroes of the quadratic polynomial 3x2 – kx + 6 is 3, then find the value of k.
2. If the sum of the zeroes of the polynomial p(x) = (k2 – 14) x2 – 2x – 12 is 1, then find the value of k. 
3. If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.
4. A quadratic polynomial, whose zeroes are -4 and -5, is …. ?
5. If α and β are zeroes of p(x) = kx2 + 4x + 4, such that α2 + β2 = 24, find k.
6. If p(x) = x3 – 2x2 + kx + 5 is divided by (x – 2), the remainder is 11. Find k. Hence find all the zeroes of x3 + kx2 + 3x + 1.
7. Find all the zeroes of the polynomial 8x4 + 8x3 – 18x2 – 20x – 5, if it is given that two of its zeroes are 52−−√ and −52−−√
8. If a polynomial x4 + 5x3 + 4x2 – 10x – 12 has two zeroes as -2 and -3, then find the other zeroes.
9. If a polynomial x4 + 5x3 + 4x2 – 10x – 12 has two zeroes as -2 and -3, then find the other zeroes.
10. Divide 4x3 + 2x2 + 5x – 6 by 2x2 + 1 + 3x and verify the division algorithm.