How many solutions does #-12x^2-4x+5=0# have?

2 Answers
Mar 5, 2018

Answer:

Two

Explanation:

It can only have 2 or less solutions because the highst power of x is 2 (#-12x^color(blue)(2)#). Lets check if it has 2, 1 or no solutions:

#-12x^2-4x+5=0|:(-12)#
#x^2+1/3x-5/12=0#
#color(blue)(x^2+1/3x+1/36)color(red)(-1/36-5/12)=0#
#color(blue)((x+1/6)^2)color(red)(-16/36)=0|+16/36#
#(x+1/6)^2=16/36|sqrt()#
#x+1/6=+-2/3|-1/6#
#x=+-2/3-1/6#
#x_1=1/2 or x_2=-5/6#

Mar 5, 2018

Answer:

Method shown below, you do the math.

Explanation:

Rewrite the equation, change signs on both side:

#12x^2 +4x -5 =0#
This can be seen to be the familar quadratic equation

#ax^2 +bx +c# with a solution:

#x= ( -b +- sqrt(b^2 -4ac))/(2a)#

Substitute values to a, b, c to get the answer