The value of the discriminant is the value of [tex] b^{2} -4ac[/tex] located inside the square root of the quadratic formula. To find this, we simply look at the quadratic equation in standard form: [tex]a x^{2} +bx+c=0[/tex] and plug in the existing values into the quadratic formula ([tex] \frac{-b+- \sqrt{ b^{2}-4ac } }{2a} [/tex]. Plug in the values of a b and c (2, 7, and -4, respectively) and get [tex] \frac{-7+- \sqrt{49-4(2)(-4)} }{4} [/tex].
Simplifying this, we get
[tex] \frac{-7+- \sqrt{81} }{4} = \frac{-7+-9}{4} = \frac{2}{4} or \frac{-16}{4} [/tex]
which equal 1/2 and -4, respectively.
A )The value of the discriminant is 81 (see work above)
B ) 2 solutions, discriminant is positive, and not equal to zero. They are both rational since sqrt 81 is a rational number
C ) 1/2 and -4 (see work above)
