KVPY SX SB Exam 2013 Question Paper

Question : 1 of 120

Marks: +1, -0

Part-I

MATHEMATICS

The sum of non-real roots of the polynomial equation

x^3+3x^2+3x+3=0

Solution:

f(x) = x^3 + 3x^2 + 3x + 3 = 0

f'(x) = 3x^2 + 6x + 3

= 3(x + 1)^2 ≥ 0

f(x) is Increasing function
Now

f(- 3) = - 6 < 0

f(- 2) = 1 > 0

∴ real root

γ

lies between - 3 and -2

\α + \β + \γ = - 3

;

- 3 < \γ < - 2

α + \β - 3

< α + \β + \γ <

α + \β - 2

α + \β - 3 < - 3 < α +\β - 2

- 1 < α + \β < 0

Go to Question:

Next Question