Question

If α, β, γ are the zeros of the given cubic polynomials, find the values as given in the table.
S.No. Cubic Polynomial α + β + γ αβ + βα + γα αβγ
1 x³ + 3x² – x – 2
2 4x³ + 8x² – 6x – 2
3 x³ + 4x² – 5x – 2
4 x³ + 5x² + 4

Answer 1

Hi ,

1. x³ + 3x² - x -2 compare with ax³ + bx² + cx + d

   a = 1 , b = 3 , c = -1 , d = -2

α + β + γ = -b/a = ( - 3 ) /1 = -3

αβ + βγ + γα = c/a = ( -1 )/1 = -1

αβγ = -d/a = - ( -2 )/1 = 2

2 ) 4x³+8x²-6x-2 compare with ax³+bx²+cx +d

a = 4 , b= 8 , c = -6 , d = -2

α+β+γ = -b/a = -8/4 = -2

αβ+βγ+γα = c/a = ( -6)/4 = -3/2

αβγ = -d/a = - ( -2 )/4 = 1/2

3 ) x³+4x²-5x-2 compare with ax³+bx²+cx+d

a = 1 , b= 4 , c= -5 , d= -2

α+β+γ = -b/a = - 4/1 = -4

αβ+βγ+γα = c/a = ( -5 )/1 = -5

αβγ = -d/a = - (-2 )/1 = 2

4 ) x³+5x²+4 compare with ax³+bx²+cx+d

a = 1 , b= 5 , c =0 , d= 4

α+β+γ = -b/a = -5/1 = -5

αβ+βγ+γα = - c/a = - 0/1 = 0

αβγ = -d/a = - ( 4 )/1 = -4

I hope this helps you.

: )