# FIND EQUATION OF CUBIC POLYNOMIAL FROM ZEROS WORKSHEET

Find all cubic polynomials with zeros of :

Problem 1 :

±2, 3

Solution

Problem 2 :

-2, ± i

Solution

Problem 3 :

3, -1 ± i

Solution

Problem 4 :

-1, -2 ± √2

Solution

1)  a(x2 - 4) (x - 3)

2)  a(x2 - 4) (x - 3)

3)  a(x - 3) (x2 + 2x + 2)

4)  a(x + 1) (x2 + 4x + 2)

Problem 1 :

Find all third degree real polynomials with zeroes of -1/2 and 1-3i.

Problem 2 :

p(x) is a real cubic polynomial in which p(1) = p(2 + i) = 0 and p(0) = -20. Find p(x) in expanded form.

Problem 3 :

5 - i is a zero of 2z3 + az2 + 62z + (a - 5), where a is real. Find a and other two zeroes.

Problem 4 :

-2/3 and 2 are zeroes of 6x3 + ax2 - 4ax + b. Find the value of a and b.

1)  y = a (2x + 1)(x2 - 2x + 10), where a ≠ 0

2)  y = 4(x - 1)(x2 - 4x + 5)

3)  z = -1/2

4)  a = 7 and b = -20

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