Question

Find the cubic equation whose leading coefficient is 1 with real coefficient whose two roots are 2-5i and 5. Person with most appropriate answer will be marked BRAINLIEST!!!!!

Answer 1

Given: Two roots : 2-5i and 5

To find: The cubic equation whose leading coefficient is 1 with real coefficient.

Solution:

• Now we have given the roots are:

                 2-5i , the second root must be 2 + 5i and third root is 5.

• Lets consider two roots:

                 2 - 5i and 2 + 5i

• Sum of roots: 2 - 5i + 2 + 5i = 4

• Product of roots: 2 - 5i x 2 + 5i = 4 - 25(i)^2 = 4 + 25 = 29

• The equation will be:

                 x² - 4x + 29

• Now lets consider the third root 5, we get:

                 (x² - 4x + 29)(x - 5)

• Expanding it, we get:

                 x³ - 4x² + 29x - 5x² + 20x - 145 = 0

                 x³ - 9x² + 49x - 145 = 0

Answer:

           So the cubic equation is x³ - 9x² + 49x - 145 = 0