Question

one root of the cubic equation x^3 - 6x^2 + 11 = 0 is 3 and one of the other two root is twice the other. find the other tow roots.

Answer 1

Correct Question :

One root of the cubic equation x³ - 6x² + 11x - 6 = 0 is 3 and one of the other two roots is twice the other. Find the other two roots.

Answer :

The other two roots are 1 and 2.

Step-by-step explanation :

⇒ Cubic Polynomial :

• It is a polynomial of degree 3.

• General form :

       ax³ + bx² + cx + d

• Relationship between zeroes and coefficients :

        ☆ Sum of zeroes = -b/a

        ☆ Sum of the product of zeroes taken two at a time = c/a

        ☆ Product of zeroes = -d/a

_______________________________

Given

• cubic equation, x³ - 6x² + 11x - 6 = 0

 It is of the form ax³ + bx² + cx + d = 0

    a = 1 , b = -6 , c = 11 , d = -6

• One root = 3
• One of the other two roots is twice the other

To find,

• the other two roots

   Let one of the two roots be "p"

     Then the other root = 2p

we know,

Sum of roots = -b/a

  3 + p + 2p = -(-6)/1

  3 + 3p = 6

    3p = 6 - 3

    3p = 3

     p = 3/3

     p = 1

⇒ 2p = 2(1) = 2

∴ The other two roots are 1 and 2.