How do you use the discriminant to determine the nature of the solutions given # –4p^2 – 1.8p + 0.2 = 0#?

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Answer 1 · 2017-01-14T14:28:12

The solutions are #={-0.54,0.09}#

We compare this equation to

#ax^2+bx+c=0#

#-4p^2-1.8p+0.2=0#

The discriminant is

#Delta=b^2-4ac=(-1.8)^2-4*(-4)*(0.2)#

#=3.24+3.2=6.44#

As #Delta >0#, we have 2 real roots

#p_1=(1.8+sqrt6.44)/(2*-4)=(1.8+2.54)/-8=-0.54#

#p_2=(1.8-sqrt6.44)/(2*-4)=(1.8-2.54)/-8=0.09#