3x² - 7x - 8 = 0
We're asked about square roots so we won't try to factor; we'll go right for the quadratic formula,
x = ( 7 ± √(7² - 4(3)(-8)) )/(2(3)) = (7 ± √(49+96))/6 = 7/6 ± √145/6
145 = 5×29, so no square factors. The positive difference is
d = (7/6 + √145/6) - (7/6 - √145/6) = 2√145/6 = √145/3
so m=145, n=3 for a sum of
Answer: 148
Complex solutions, namely roots with a √(-1) or "i" in it, never come all by their lonesome, because an EVEN root like the square root, can have two roots that will yield the same radicand.
a good example for that will be √(4), well, (2)(2) is 4, so 2 is a root, but (-2)(-2) is also 4, therefore -2 is also a root, so you'd always get a pair of valid roots from an even root, like 2 or 4 or 6 and so on.
therefore, complex solutions or roots are never by their lonesome, their sister the conjugate is always with them, so if there's a root a + bi, her sister a - bi is also coming along too.
if complex solutions come in pairs, well, clearly a cubic equation can't yield 3 only.
Answer: Third option.
Step-by-step explanation:
Let be "x" the approximate actual width (in feet) of the car.
Based on the information provided in the exercise, you know that the scale of the model car is this one:
Which can be written as a fraction:
Therefore, if you know that the width of the model car is 2.3 inches, you can set up the following proportion:
Finally, you must solve for "x" in order to find its value.
So you get the following result:
To rent 7 movies, he needs 2(7) + 12 = $26.
But he has only $10. So he needs more 26 - 10 = $16.
