Question

Find the equation each of whose roots is greater by unity than a root of the equation x35x2+6x3=

Answer 1

Answer:

Step-by-step explanation:

Given Find the equation each of whose roots is greater by unity than a root of the equation  x^3 – 5x^2 + 6x – 3 = 0

Given equation is x^3 – 5x^2 + 6x – 3 = 0

We need to replace x as x – 1 in order to obtain an equation each of whose root is greater by a unity.

So (x – 1)^3 – 5(x – 1)^2 + 6(x – 1) – 3 = 0

We know that

(a – b)^3 = a^3 – b^3 – 3a^2b + 3ab^2

(a – b)^2 = a^2 + b^2 – 2ab

So x^3 – 1 – 3x^2 + 3x – 5(x^2 + 1 – 2x) + 6x – 6 – 3 = 0

Implies x^3 – 1 – 3x^2 + 3x – 5x^2 – 5 + 10 x + 6 x – 6 – 3 = 0

         So x^3 – 8x^2 + 19 x – 15 = 0

Answer 2

Hey, here is your answer!!