Question

Iif alpha =3 beta =6 gamma=2 write a cubic polynomial

Answer 1

Here I am writing alpha as a, beta as b, and gamma as c.

Given f(x) = x^3 - 12x^2 + 44x + c.

Given that a + c = 2b----- (1)

We know that sum of the roots = -b/a

 a + b + c = -(-12)/1

               = 12  ------ (2)

ab + bc + ca = c/a

                    = 44/1

                    = 44    ------------- (3)

abc = -d/a

      = -c/1

      = -c   ------- (4)

From (1) & (4), we get

 = > 2b + b  = 12.

= > 3b = 12

= > b = 4   ------- (5)

Substitute b = 4 in (1), we get

= > a + c = 2b

= > a + c = 2(4)

= > a + c = 8.   ------- (6)

Substitute (5) in (4), we get

= > a(4) * c = -c

= > ac = -c/4    ------- (7)

On solving equation (3), we get

= > ab + bc + ca = 44

= > b(a + c) - c/4 = 44

= > b(8) - c/4 = 44

= > 32 - c/4 = 44

= > -c/4 = 44 - 32

= > -c/4 = 12

= >c = -48.

Therefore the value of c = -48

Answer 2

mark me as a brainielist