Find the zeros of the function. f(x) = 9x2 - 12x - 5

Question

Find the zeros of the function.  f(x) = 9x2 - 12x - 5

anonymous · Answer

set it equal to zero $$9x^2 - 12x - 5 = 0 $$ then factor it

anonymous · Answer

I got x = (-1/3) and x = (5/3)

triciaal · Answer

9x^2-12^2x -5 =0
quadratic formula
a = 9 b = -12 c = -5

12 +/- rt [144 -(4)(9)(-5)} / 18
(12+/- 18)/18 
5/3 and -1/3

anonymous · Answer

It also factors into (3x+1)(3x-5)

set each to 0, and you get the answer above

anonymous · Answer

ok thanks a lot

whpalmer4 · Answer

@Anonymous1321
You didn't do the factoring quite right — when you wrote it as $$(9x-15)(9x+3)$$you introduced a spurious factor of 9.  If you expand that product, you get$$9x*9x+9x*3 -15*9x -15 *3  = 81x^2-108x -45$$which is not what you started with.

Proper factoring:
$$9x^2-12x-5$$$$9*-5 = -45$$Find pair of factors of -45 that sum to -12, -15 and 3 are such a pair, so write
$$9x^2 - 15x + 3x - 5$$Group terms$$(9x^2-15x)+(3x-5)$$Factor each group$$3x(3x-5)+1(3x-5)$$Notice common factor and factor again$$(3x-5)(3x+1)$$Solve for roots$$3x-5=0\rightarrow x=\frac{5}{3}$$$$3x+1=0\rightarrow x=-\frac{1}{3}$$