QQuestionAnatomy and Physiology
QuestionAnatomy and Physiology
Open parenthesis, a x plus 3, close parenthesis, times, open parenthesis, 5 x squared, minus b x, plus 4, close parenthesis, equals, 20 x cubed, minus 9 x squared, minus 2 x, plus 12
The equation above is true for all $x$, where $a$ and $b$ are constants. What is the value of $a b$ ?
A. 18
B. 20
C. 24
D. 40
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Answer
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Step 1:: Compare the given equation to the general form of a quadratic equation.
(ax+3)(5x^2-bx+4) = 20x^3-9x^2-2x+12
The given equation is in the form of a factored quadratic, which can be written as:
Step 2:: Expand the left side of the equation.
ax(5x^2) + ax(-bx) + ax(4) + 3(5x^2) + 3(-bx) + 3(4) = 20x^3-9x^2-2x+12
Expand the product on the left side of the equation:
Step 3:: Simplify and rearrange the left side of the equation.
5ax^3 - abx^2 + 4ax + 15x^2 - 3bx + 12 = 20x^3-9x^2-2x+12
Simplify the equation:
Step 4:: Compare the coefficients of like terms on both sides of the equation.
-ab + 15 = -9 \Rightarrow -4b + 15 = -9 \Rightarrow b = 6
Step 5:: Calculate the product $ab$.
ab = 4 \times 6 = 24
Final Answer
The value of $ab$ is 24, which corresponds to option C.
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