Consider only the discriminant, $b ^ { 2 } - 4 a c$ to determine whether one real-number solution, two different real-number
solutions, or two different imaginary-number solutions exist.
-$$7 x ^ { 2 } = 21 x$$
A) 3
B) $10.5$
C) 7,3
D) 0,3

Question

Quizplus · Accepted Answer

The given equation is $7x^2 = 21x$, which can be rewritten as $7x^2 - 21x = 0$. Comparing this with the standard quadratic equation $ax^2 + bx + c = 0$, we have $a = 7$, $b = -21$, and $c = 0$. The discriminant is $b^2 - 4ac = (-21)^2 - 4(7)(0) = 441 - 0 = 441$. Since the discriminant is positive, there are two different real-number solutions. However, the choices provided seem to misunderstand the question's intent, focusing on the coefficients and the discriminant's outcome rather than the discriminant's interpretation. The correct interpretation is that a positive discriminant indicates two different real-number solutions, but none of the choices directly reflect this understanding. The choice "D" is marked correct because it's the only one that directly relates to the components of the discriminant calculation, albeit incorrectly framed in the context of the question's actual ask.

Consider Only the Discriminant b2−4acb ^ { 2 } - 4 a cb2−4ac

Consider Only the Discriminant $b ^ { 2 } - 4 a c$