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Solve the following equations : x^4 – 2x^3 + 4x^2 + 6x – 21=0 x^4 – 2x^2 + 8x – 3=0

Solve the following equations : 
  1. x^4 – 2x^3 + 4x^2 + 6x – 21=0
  2. x^4 – 2x^2 + 8x – 3=0

Grade:11

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
Hello student,
Please find the answer to your question below
1.x4-2x3+4x2+6x-21=0
x4-2x3=-4x2+6x-21
Adding x2on both sides we get
(x2-x)2=-3x2-6x-21
(x2-x+y)2=x2(-3+2y)+x(-2y-6)+y2+21
by putting y=2 we get perfect square on RHS
so (x2-x+2)2=(x-5)2
it is in the form of a2-b2=0
Hence we get a+b=0;a-b=0
so x2-3=0 and x2-2x+7=0
we get x=\pm \sqrt{3},1\pm \sqrt{6}i
(2) let x4-2x2+8x-3=(x2+ax+b)(x2+cx+d)
we get on solving a=-2,b=3,c=2,d=-1
So x4-2x2+8x-3=(x2-2x+3)(x2+2x-1)
on solving above 2 quadratic equations we get x=\sqrt{2}-1,-\sqrt{2}-1,1-\sqrt{2}i,1+\sqrt{2}i

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