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$5x^{2}-37x-24=0$
What is the positive solution to the given equation?
Difficulty: Medium
A:
$\frac{3}{5}$
B:
$3$
C:
$8$
D:
$37$
The expression $4x^{2}+bx-45$, where $b$ is a constant, can be rewritten as $(hx+k)(x+j)$, where $h$, $k$, and $j$ are integer constants. Which of the following must be an integer?
Difficulty: Hard
A:
$\frac{b}{h}$
B:
$\frac{b}{k}$
C:
$\frac{45}{h}$
D:
$\frac{45}{k}$
$$y=0.25x^{2}-7.5x+90.25$$
The equation gives the estimated stock price $y$ in dollars, for a certain company $x$ days after a new product is launched, where $0\leq x\leq 20$. Which statement is the best interpretation of $(x,y)=(1,83)$ in this context?
Difficulty: Medium
A:
The company's estimated stock price increased $83 every day after the new product launched.
B:
The company's estimated stock price increased $1 every 83 days after the new product launched.
C:
1 day after the new product launched, the company's estimated stock price is $83.
D:
83 days after the new product launched, the company's estimated stock price is $1.
$(x-1)^{2}=-4$
How many distinct real solutions does the given equation have?
Difficulty: Hard
A:
Exactly one
B:
Exactly two
C:
Infinitely many
D:
Zero
Which expression is a factor of $2x^{2}+38x+107$
Difficulty: Easy
A:
$2$
B:
$5x$
C:
$38x$
D:
$2x^{2}$
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