POLYNOMIALS DPP
1) Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes, respectively.
(i) 1/4, -1
(ii) 1,1
(iii) 4, 1
(i) 1/4, -1
(ii) 1,1
(iii) 4, 1
2) How many zeros does the polynomial (x – 3)2 – 4 can have? Also, find its zeroes.
3) Find the value of “x” in the polynomial 2a2 + 2xa + 5a + 10 if (a + x) is one of its factors.
4) Find the quadratic polynomial if its zeroes are 0, √5.
5) Compute the zeroes of the polynomial 4x2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.
6) Find the value of “p” from the polynomial x2 + 3x + p, if one of the zeroes of the polynomial is 2.
7) α and β are zeroes of the quadratic polynomial x2 – 6x + y. Find the value of ‘y’ if 3α + 2β = 20.
8) Does the polynomial a4 + 4a2 + 5 have real zeroes?
9) If the zeroes of the polynomial x3 – 3x2 + x + 1 are a – b, a, a + b, then find the value of a and b.
10) If α and β are the zeroes of the polynomial ax2 + bx + c, find the value of α2 + β2