You can put this solution on YOUR website! Giving you some tricky questions are they? I think we can handle it. It just a little complicated on-line.
First, to reduce the order of the polynomial, let
(1) y = x^2, then your equation reduces to
(2) y^2 + sqrt(76)*y -76 = 0
Now use the quadratic equation to find the roots of (2).
(3) y = or
(4) y = or
(5) y = or
(6) y =
Since y = x^2 we get
(7) x = +/-sqrt(y) and since y has two roots we will get four roots for x.
Taking the square root of (6) gives us two roots of x
(8) and
(9)
Likewise we can write the other two roots of x as
(10) and
(11)
We acn check these roots by substitution into your original equation in x. I'll use x of (8) to show that
(12)
We have
(13) and
(14)
Now put (13) and (14) into (12) and get
(15) or
(16)
Multiply (16) by 4/76 and get
(17) or
(18) or
(19) or
(20) or
(21) or
(22) 0 = 0 check
Answers: the roots of your quardic equation are given by (8)-(11)
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