Question

9x^4-27x^2+20=0
help please? gold medal to the person that works it out for me!

Answer 1

Try the AC method to factor the left hand side.
9x^4-27x^2+20=0
a = 9, b = -27, c = 20
a * c = 9 * 20 = 180
See if you can find factors of 180 that add to -27. Obviously both factors have to be negative here.

Answer 2

Or split -27 into two parts that add to -27 and multiplies to +180.

Answer 3

How do I split it?

Answer 4

-15 and -12

Answer 5

So then how would the equation look then? 9x^4-15-12+20=0?

Answer 6

Oops 9x^4-15x-12x+20

Answer 7

9x^4-27x^2+20=0
9x^4-12x^2-15x^2+20=0
3x^2(3x^2-4) -5(3x^2-4) = 0
(3x^2-5)(3x^2-4) = 0
3x^2 - 5 = 0 or 3x^2 - 4 = 0
3x^2 = 5 or 3x^2 = 4
x^2 = 5/3 or x^2 = 4/3
\(\large x = -\sqrt{\frac 53}; ~~~~x = \sqrt{\frac 53}; ~~~~
x = -\sqrt{\frac 43}=-2\sqrt{\frac 13}; ~~~~x = \sqrt{\frac 43} =2\sqrt{\frac 13}\)

Answer 8

thank you!