Show all steps for full credit Find all the real zeros of Fx

Show all steps for full credit: Find all the real zeros of F(x) = 3x^4 + 6x^2 - 12 simply Difference Quotient of F(x) = 1/ squareroot 5-x

Solution

1)given F(x)= 3x⁴+6x²-12

let us substitute x²=p

=>x⁴=p²

F(p)= 3p²+6p-12

for zeroes

3p²+6p-12=0

3(p²+2p-4)=0

p²+2p-4=0

p²+2p=4

p²+2p+1=4+1

p²+2p+1=5

(p+1)²=5

p+1=-5 ,p+1=5

p=-1-5 ,p=-1+5

x²=-1-5, x²=-1+5

x²=-1-5 => x doesnot have real values

x²=-1+5

x=-(-1+5),x=(-1+5) are the real zeroes

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