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find roots of x^3 - 2x^2 +1 if one root is 1?


Aryan Mittal 12th Jul, 2020
Answers (2)
Vaishali Sharma 12th Jul, 2020
Hello,
Divide the whole equation by (x-1)  as 1 is the root of the equation. Then you'll get a quadratic equation.
Factorise the quadratic equation, which gives you 2 remaining roots.
Rishi Garg 12th Jul, 2020

Let other roots be a and b.

Now, a+b+1 = 2 which gives  a+b = 1

and a.b.1 = -1 which gives ab = -1

putting a = 1 - b from the first equation in the second, we get

(1-b)b = -1

Solving the above equation, we get b = (1+\root(5))/2 and b = (1-\root(5))/2

hence, the other two roots are (1+\root(5))/2 and (1-\root(5))/2.

Hope this helps.

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