How do you use the discriminant to determine the nature of the roots for -6x^2 - 12x + 90 = 0?

1 Answer
Don't Memorise
Jun 19, 2015

As here, Delta>0 and a perfect square there are two real rational roots.

Explanation:

-6x^2 -12x +90 = 0
The equation is of the form color(blue)(ax^2+bx+c=0 where:
a=-6, b=-12, c=90

The Discriminant is given by:
Delta=b^2-4*a*c
= (-12)^2-(4*(-6)*90)
= 144+2160 =2304

As here, Delta>0 and it is also a perfect square there are two real rational roots.

  • Note :
    The solutions are normally found using the formula
    x=(-b+-sqrtDelta)/(2*a)

As Delta = 2304, x = (-(-12)+-sqrt(2304))/(2*-6) = (12+-48)/-12
x = (12-48)/-12 = 36/12= color(green)(3
x = (12+48)/-12 = -60/12 =color(green)( -5

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