Answer:-
newton's method - http://math.tutorvista.com/calculus/newton-raphson-method.html to find the largest positive solution is
f(x)=x^4-7x^2-8
f'(x) = 4x^3 -14x
Start out with an initial value x0=4
x1 = x0- f(x0)/f'(x0)
x1 = 4 - f(4)/f'(4)
x1 = 4 - 136/200 = 3.32
x2 = x1 - f(x1)/f'(x1)
x2 = 3.32 - f(3.32) /f'(3.32)
x2 = 3.32 - 36.3365 / 99.8975
x2 = 2.95626205
Proceed this way for 6 more iterations.
x = 2.95626205 7.2022062431
x = 2.84001712 0.5955914357
x = 2.82853399 0.0054411498
x = 2.82842713 4.682e-70000
x = 2.82842712 0.0000000000
x=2.82842712
+4 
+16 
