SOLUTION: find roots : 4x^4-37x^2+9=0

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Question 294188: find roots : 4x^4-37x^2+9=0
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Find the roots of 4x%5E4-37x%5E2%2B9+=+0
Let's do a temporary change of variable to make this look like a quadratic equation by substituting x%5E2+=+y:
4y%5E2-37y%2B9+=+0 Solve by factoring.
%284y-1%29%28y-9%29+=+0 Apply the "zero product" rule:
4y-1+=+0 or y-9+=+0 and so...
4y+=+1 or y+=+9 Re-substitute y+=+x%5E2.
highlight%284x%5E2+=+1%29 or highlight_green%28x%5E2+=+9%29 Take the square root of both sides.
highlight%282x+=+1%29 or highlight%282x+=+-1%29 or highlight_green%28x+=+3%29 or highlight_green%28x+=+-3%29
Finally, the four roots are:
highlight%28x+=+1%2F2%29
highlight%28x+=+-1%2F2%29
highlight_green%28x+=+3%29
highlight_green%28x+=+-3%29
Verify by graphing:
graph%28400%2C400%2C-5%2C5%2C-80%2C30%2C4x%5E4-37x%5E2%2B9%29