Answer :

(1) The quadratic polynomial is,

p(x) = ax^{2} + bx + c; a ≠ 0, a, b, c ε R.

∴ Substituting a = 6, b = 17 and c = 11, we get the required quadratic polynomial

p(x) = 6x^{2} + 17x + 11.

(2) The cubic polynomial is,

p(x) = ax^{3} + bx^{2} + cx + d; a ≠ 0, a, b, c, d ε R.

∴ Substituting a = 1, b = —1, c = —1 and d = 1, we get the required cubic polynomial

p(x) = x^{3} – x^{2} – x + 1.

(3) The quadratic polynomial is,

p(x) = ax + bx + c; a ≠ 0, a, b, c ε R.

∴ Substituting a = 5, b = 7 and c = 2, we get the required quadratic polynomial

p(x) = 5x^{2} + 7x + 2.

(4) The cubic polynomial is,

p(x) = ax + bx + cx + d; a ≠ 0, a, b, c, d ε R.

∴ Substituting a = 1, b = –3, c = –1 and d = 3, we get the required cubic polynomial

p(x) = x^{3} – 3x^{2} – x + 3.

(5) The cubic polynomial is,

p(x) = ax^{3} + bx^{2} + cx + d; a ≠ 0, a, b, c, d ε R.

∴ Substituting a = 3, b = –5, c = –11 and d = –3, we get the required cubic polynomial

p(x) = 3x^{3} – 5x^{2} – 11x – 3.

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