if 4x²+17x + m-3/5=0 has repeated roots. find the value of m
Answers
What are the roots of the equation x4−4x3+8x2−8x+4=0 ?
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x^4-4x^3+8x^2-8x+4 =0 can be written as
x^4-4x^3+(4x^2+4x^2)-8x+4=0 {8x^2=4x^2+4x^2}
Now group the part of the equation in this manner.
x^2(x^2-4x+4)+4(x^2-2x+1)=0
x^2(x-2)^2+4(x-1)^2=0
we can see that (x(x-2))^2 and (2(x-1))^2 would always be positive.
So to get the sum equal to zero we need both the parts to be equal to zero simultaneously. But this cannot be possible in this case so real roots do not exist in this case, we have to find imaginary roots.
x^2(x-2)^2=-4(x-1)^2
(x^2(x-2)^2)/(x-1)^2=-4
((x^2-2x)/x-1)^2=-4
((x^2-2x)/x-1)=+-2i
solve for this equations