How do you use the discriminant to determine the nature of the solutions given #y = 9x + 3 – 5x^2#?

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Answer 1 · 2017-08-19T11:39:00

Solution: # x ~~ 2.087 , x ~~ -0.287 #

#y= -5x^2 +9x +3 # . Comparing with standard quadratic equation

#ax^2+bx+c =0 # here # a =-5 , b=9 ,c = 3#. We know

discriminant of a quadratic equation is #D = b^2-4ac #

#= 9^2- 4*(-5)*3 = 141 # ,here discriminant is positive,

so we will get two real solutions.

The solutions can be calculated by using quadratic formula.

# x = (-b +- sqrt D)/(2a) = (-9 +- sqrt141)/ -10 = 0.9 +- 1.187 # or

# x ~~ 2.087 , x = -0.287 # [Ans]