Home
Class 12
MATHS
The sum of all the real roots of equatio...

The sum of all the real roots of equation `x^4-3x^3-2x^2-3x+1=0` is

Text Solution

Verified by Experts

`x^4-3x^3-2x^2-3x+1 = 0`
`(x^2-4x+1)(x^2+x+1) = 0`
Now, roots of equation,`x^2-4x+1 = 0`,
`x = (4+-sqrt(16-4))/2 = 2+-sqrt3`
These are real roots.
Now, roots of equation,`x^2+x+1 = 0`,
`x = (-1+-sqrt(1-4))/2 = -(1+-sqrt(-3))/2`
These are imaginary roots.
...
Promotional Banner

Similar Questions

Explore conceptually related problems

The sum of all real roots of the equation |x-3|^(2)+|x-3|-2=0

Number of distinct real roots of equation 3x^4+4x^3-12x^2+4=0

The number of real roots of the equation x^(4)+x^(3)+2x^(2)+x+1=0 is

Find the sum of all the real roots of the equation P(x)= 2x^98+3x^97+2x^96+…….+2x+3=0 .

The real roots of the equation |x|^3-3x^2+3|x|-2=0 are

The sum of the real roots of the equation x^(5)-5x^(4)+9x^(3)-9x^(2)+5x-1=0 is

The sum of the real roots of the equation x^(5)-5x^(4)+9x^(3)-9x^(2)+5x-1=0 is

For x in R the number of real roots of the equation 3x^2-4abs(x^2-1)+x-1=0 is ______

The real roots of the equation |x|^(3)-3x^(2)+3|x|-2=0