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]

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