Find a cubic polynomial whose zeroes are 1/2, 1 and -3.

1.	Find a cubic polynomial whose zeroes are 1/2, 1 and -3.
Answer» General form of a cubic polynomial whose zeroes are a, b and c is: x³ – (a + b + c) x² + (ab + bc + ca)x – abc …(1) To Find: Cubic polynomial whose zeroes are 1/2, 1 and -3 Let us say, a = 1/2, b = 1 and c = -3 Putting the values of a, b and c in the equation (1) we get: = x³ – (1/2 + 1 – 3) x² + (1/2 – 3 – 3/2)x – (- 3/2) = x³ – (-3/2) x² – 4x + 3/2 = 2x³ + 3x² – 8x + 3 Which is required polynomial.

Answer»

General form of a cubic polynomial whose zeroes are a, b and c is:

x³ – (a + b + c) x² + (ab + bc + ca)x – abc …(1)

To Find: Cubic polynomial whose zeroes are 1/2, 1 and -3

Let us say, a = 1/2, b = 1 and c = -3

Putting the values of a, b and c in the equation (1) we get:

= x³ – (1/2 + 1 – 3) x² + (1/2 – 3 – 3/2)x – (- 3/2)

= x³ – (-3/2) x² – 4x + 3/2

= 2x³ + 3x² – 8x + 3

Which is required polynomial.

Discussion