no. of real roots of the equation x^4 + 3x^3 - 6x^2 + 5x + 4 = 0 will be

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18 Sep 2012 equation

no. of real roots of the equation
x^4 + 3x^3 - 6x^2 + 5x + 4 = 0
will be

OPtion

1) 0
2) 1
3) 2
4) 3
5) 4
6) 5
7) none of these

Solution

x^4 + 3x^3 - 6x^2 + 5x + 4 = 0
there are 2 times sign conversion
first in + 3x^3 - 6x^2
and second in - 6x^2 + 5x
so 2 real positive roots are there
similarly
take -x in place of x
we will get x^4 - 3x^3 - 6x^2 - 5x + 4 = 0
there are 2 times sign conversion again
first in x^4 - 3x^3
and second in - 5x + 4
so 2 real negative roots are there
total real roots = 4

Correct Option: 5 Best Solution (0)