Polynomial & Real Number
1.Find the zeros of each of the following quadratic polynomials and verify the
relationship between the zeros and their coefficients:
(a) 2s2 – (1 + 2√2)s + √2 ans √2 & 1/2 (b) g(x)=a(x2+1)–x(a2+1). Ansa & 1/a.
2. For each of the following, find a quadratic polynomial whose sum and
product, respectively, of the zeros are as given. Also, find the zeros of these
polynomials by factorisation.
-3/2√5, -1/2. Ans , -√5/2 and 1/√5.
3.If α and β are the zeroes of the quadratic polynomial f(x) = x2 + x – 2, find the value of 1/α
– 1/β. (Ans 3/2)
4. If one of the zeros of the quadratic polynomial f(x) = 4x2 – 8kx – 9 is negative of the
other, then find the value of k. (Ans -0)
5. If the sum of the zeroes of the quadratic polynomial f(t)=kt2 + 2t + 3k is equal to their
product, then find the value of k. (Ans-2/3)
6. If α and β are the zeros of the quadratic polynomial f(t)=t2– 4t + 3, find the value
of α4β3+α3β4.
7. Verify that the numbers given alongside the cubic polynomials below are
their zeroes. Also, verify the relationship between the zeros and coefficients in
each of the following cases: g(x) = x3 – 4x2 + 5x – 2; 2, 1,
8. An army contingent of 616 members is to march behind an army band of
32 members in a parade. The two groups are to march in the same number of
1.Find the zeros of each of the following quadratic polynomials and verify the
relationship between the zeros and their coefficients:
(a) 2s2 – (1 + 2√2)s + √2 ans √2 & 1/2 (b) g(x)=a(x2+1)–x(a2+1). Ansa & 1/a.
2. For each of the following, find a quadratic polynomial whose sum and
product, respectively, of the zeros are as given. Also, find the zeros of these
polynomials by factorisation.
-3/2√5, -1/2. Ans , -√5/2 and 1/√5.
3.If α and β are the zeroes of the quadratic polynomial f(x) = x2 + x – 2, find the value of 1/α
– 1/β. (Ans 3/2)
4. If one of the zeros of the quadratic polynomial f(x) = 4x2 – 8kx – 9 is negative of the
other, then find the value of k. (Ans -0)
5. If the sum of the zeroes of the quadratic polynomial f(t)=kt2 + 2t + 3k is equal to their
product, then find the value of k. (Ans-2/3)
6. If α and β are the zeros of the quadratic polynomial f(t)=t2– 4t + 3, find the value
of α4β3+α3β4.
7. Verify that the numbers given alongside the cubic polynomials below are
their zeroes. Also, verify the relationship between the zeros and coefficients in
each of the following cases: g(x) = x3 – 4x2 + 5x – 2; 2, 1,
8. An army contingent of 616 members is to march behind an army band of
32 members in a parade. The two groups are to march in the same number of
