Q3 of 113 Page 60

Find a cubic polynomial whose zeros are 2, –3 and 4

Let the zeros of the polynomial be a, b and c

Where a = 2, b = - 3 and c = 4


The cubic polynomial can be calculated as follows:


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


Putting the values of a, b and c in the above equation we get:


= x3 – (2 – 3 + 4) x2 + (-6 – 12 + 8) x – (- 24)


= x3 – 3x2 – 10x + 24


More from this chapter

All 113 →
1

Verify that 3, ‒2, 1 are the zeros of the cubic polynomial p(x) = x3 – 2x2 – 5x + 6 and verify the relation between its zeros and coefficients.

 2

Verify that 5, –2 and are the zeros of the cubic polynomial p(x) = 3x3 - 10x2– 27x + 10 and verify the relation between its zeros and coefficients

 4

Find a cubic polynomial whose zeros are , 1 and –3.

 5

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and the product of its zeros as 5, –2 and –24 respectively.