Compute the value of the discriminant and give the number of real solutions of the quadratic equation. -2X^2+9x-2=0

Answer 1

multiplies bt -1:

2x^2 - 9x +2 = 0

discriminant is:

b^2 - 4ac = (-9)^2 - 4(2)(2) = 81 - 16 = 65

discriminant is positive perfect square, so there are two

real but irrational roots...

they are:

x =[ 9 +or- sqrt(65) ] / 4

check

it will suffice to show that -2x^2 + 9x = 2

x^2 = (9 + sqrt(65))^2 / 16 = (81 + 18*sqrt(65) + 65)/16

= (146 + 18*sqrt(65))/16

= (73 + 9*sqrt(65))/ 8 <-- divides by 2

-2x^2 = (73 + 9*sqrt(65))/-4

9x = 81 +9*sqrt(65))/4

adding them: -2x^2 + 9x = 8/4 = 2

yes, it checks

x =[ 9 +or- sqrt(65) ] / 4