Question

solve the 4 degree equation
x^4 - 2x^3 + 4x^2 + 8x - 21 =0, given that 2 of its roots are equal in magnitude but opposite in sign.????

Answer 1

let roots be
a,-a,b,c

we have

a-a +b+c = b+c =2
also,
abc -abc -a^2 b - a^2c = -a^2(b+c) = 4

you can solve for a from here..seems it will be an imaginary root..

now you have 2 roots i.e. a and -a ..should be able to solve for other 2..

Answer 2

correction :
abc -abc -a^2 b - a^2c = -a^2(b+c) = -8 *