Answer:
Real, unequal, rational roots
Step-by-step explanation:
The key to answering this kind of question properly lies in recognizing that it is a quadratic equation and that there is a "disciminant" which tells you all you need to know, fast.
If you have ax^2 + bx + c = 0, the three coefficients of the x terms are a, b and c. The "discriminant" is defined as b^2 - 4ac.
Here we have a = 1, b = -14 and c = 24. Therefore the value of the discriminant is (-14)^2 - 4(1)(24) = 196 - 96, or 100.
Here are the rules: If the discriminant is positive we have two real, unequal roots. That's the case here.
If the discriminant is zero, we have two real, equal roots. Not here.
If the discriminant is negative, we have two complex, unequal roots. Not here.
The actual roots are found as follows: Starting with:
-b ± √[ b^2 - 4ac ]
x = ------------------------------
2a
we get:
14 ± √[ 196 - 4(1)(24)] 14 ± 10
x = --------------------------------- = ---------------
2(1) 2
Thus, x = 24/2, or 12, and x = 4/2, or 2.
We conclude that this quadratic has two real, unequal roots. We could also say "two real, unequal, rational roots."
