Answer in Algebra for Sourav Mondal #103675

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Question #103675

Use the Cauchy-Schwarz inequality to solve x³-25x²-4x+100=0, if we know
that all its roots are rational.

Expert's answer

As per the given question,

$x^3-25x^2-4x+100=0,$

Now,

$x^3-4x-25x^2+100=0,$

$x(x^2-4)-25(x^2-4)=0,$

$(x^2-4)(x-25)=0,$

so,

$x^2=4$ or $x=25$ ,

$x=\pm2$ or $x=25$ .

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Comments

Assignment Expert

16.03.20, 01:15

Cauchy-Schwarz inequality does not directly produce a solution of the problem. It just shows that x^2-4=k(x-25), where k is a constant, x^2-kx+25k-4=0. The discriminant is D=k^2-4(25k-4) and it should be a square of a rational number.

Deepak

15.03.20, 15:28

Your answer is not showing Cauchy schwarz equality