How many solutions are there to the equation 0 = 3x^2 - 10x - 5?

2 Answers
Oct 20, 2015

compare this equation with a#x^2# +bx+c=0
a= 3, b=-10, c=-5
Discriminant= #B^2# -4ac
= #(-10)^2# - 4*3(-5)
= 100+60
=160 which is more than 0
So it has two solutions.

Oct 20, 2015

Answer:

Two

Explanation:

For a quadratic in the general form:
#color(white)("XXX")ax^2+bx+c=0#
the discriminant
#color(white)("XXX")Delta = b^2-4ac#
indicates the number of solutions:
#Delta { (< 0, "no solutions"), (= 0, "exactly one solution"),(> 0, "two solutions") :}#

In this case #a=3#, #b=-10#, and #c=-5#
so #Delta = (-10)^2-4(3)(-5) = 160 > 0#
#rArr # two solutions.

Further, the discriminant is part of the quadratic formula that gives the actual solutions:
#color(white)("XXX")x = (-b+-sqrt(Delta))/(2a)#

In this case
#color(white)("XXX")x= (5+-2sqrt(10))/2#