Question

Y=6x4 + 7x2 and x = vw +1

Find the value of w when y
10.
(6 marks)
W=
Submit Answer
Skin for Now

Answer 1

w=-1/6 or w=-3

Explanation:

Substitute the value of x and y into the first equation and solve for w:

`y=6x^4+7x^2\\10=6(√(w+1))^4+7(√(w+1))^2\\10=6(w+1)^2+7(w+1)\\10=6(w^2+2w+1)+7w+7\\10=6w^2+12w+6+7w+7\\0=6w^2+19w+3`

Solve for w with the quadratic formula:

`w=(-b\±√(b^2-4ac))/(2a) \\w=(-19\±√(19^2-4(6)(3)) )/(2(6))\\w=(-19\±√(361-72))/(12) \\w=(-19\±√(289) )/(12) \\w=(-19\±17)/(12)`

After simplifying, we get either w=-1/6 or w=-3.

Not sure if w needs to satisfy all conditions while maintaining everything as real numbers, because if w=-3, then x is an imaginary number. But both values work just as fine.