- The discriminant is calculated using the formula $b^2 - 4ac$ for a quadratic equation in the form $ax^2 + bx + c = 0$.
- For problem 7: $9n^2 - 3n - 8 = -10$. First, rewrite it as $9n^2 - 3n + 2 = 0$. Here, $a=9$, $b=-3$, $c=2$. The discriminant is $(-3)^2 - 4(9)(2) = 9 - 72 = -63$. Since the discriminant is negative, there are 0 real solutions and 2 imaginary solutions.
- For problem 8: $-2x^2 - 8x - 14 = -6$. First, rewrite it as $-2x^2 - 8x - 8 = 0$. Here, $a=-2$, $b=-8$, $c=-8$. The discriminant is $(-8)^2 - 4(-2)(-8) = 64 - 64 = 0$. Since the discriminant is zero, there is 1 real solution (a repeated root) and 0 imaginary solutions.
Parent Tip: Review the logic above to help your child master the concept of using the discriminant worksheet.
