Question

2. Consider the quadratic equation 2x2 + 7x – 4 = 0.

Answer 1

The value of the discriminant is the value of $b^{2} -4ac$ located inside the square root of the quadratic formula. To find this, we simply look at the quadratic equation in standard form: $a x^{2} +bx+c=0$ and plug in the existing values into the quadratic formula ($\frac{-b+- \sqrt{ b^{2}-4ac } }{2a}$. Plug in the values of a b and c (2, 7, and -4, respectively) and get $\frac{-7+- \sqrt{49-4(2)(-4)} }{4}$.

Simplifying this, we get

$\frac{-7+- \sqrt{81} }{4} = \frac{-7+-9}{4} = \frac{2}{4} or \frac{-16}{4}$

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)