I am having some trouble with these 3 quadratic equations. I need to solve for x.
x^4+2x^2-15=0
2(x-1)^2+7(x-1)+6=0
2x-9sqrt(x)+4=0
This one factors, to give you (x^{2} + 5)(x^{2} - 3) = 0. Then solve the two quadratic factors by taking square roots.x^4+2x^2-15=0
This is just 2Y^{2} + 7Y + 6 = 0, with Y = x - 1. (You can find examples of this here.) Factor as usual, and solve the factors.2(x-1)^2+7(x-1)+6=0
This is a quadratic in sqrt[x], so you've got 2Y^{2} - 9Y + 4 = 0. Factor as usual, and then solve the factors.2x-9sqrt(x)+4=0
You should have gotten a "plus minus" sign somewhere...? To learn how this works, try here.Here's what I got for the first one,
x= i sqrt(5) and x=sqrt(3)
Factors of 12 that add to 7 are 3 and 4. To learn how to do the rest of the factorization, try here.For the second one, I can't seem to get the factors to add up to 7y (the middle term) so I'm stuck here
Factors of 8 that add to -9 are -1 and -8.For the last one, I also get stuck at factoring
Ah; so you haven't yet studied the lesson on how to factor this sort of quadratic....Wait I'm confused. For 2(x-1)^2+7(x-1)+6=0 shouldn't I be looking for factors of 6 and not 12?
And for, 2x-9sqrt(x)+4=0, don't i need factors of 4 and not 8 ?