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If r and s are constants and x2 + rx + 12 is equivalent to (x + 3)(x + s), what is the value of r ?
- a)3
- b)4
- c)7
- d)12
- e)Cannot be determined from the given information
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If r and s are constants and x2 + rx + 12 is equivalent to (x + 3)(x +...
The correct answer is c. To solve this problem, multiply the expression (x + 3) by (x + s) to get x2 + 3x + sx + 3s. You are given that x2 + rx + 12 is equivalent to x2 + 3x + sx + 3s. Therefore, 3s is equal to 12, making s equal to 4. It is also apparent that 3x + sx is equivalent to rx. Set the quantities equal and solve for r, as follows:
rx = 3x + sx
rx = x(3 + s)
r = 3 + s
Because s = 4, r must equal 7.
rx = 3x + sx
rx = x(3 + s)
r = 3 + s
Because s = 4, r must equal 7.
Most Upvoted Answer
If r and s are constants and x2 + rx + 12 is equivalent to (x + 3)(x +...
To find the value of r, we need to equate the given quadratic expression x^2 + rx + 12 with the factored expression (x + 3)(x + s).
We can expand the factored expression to get:
(x + 3)(x + s) = x^2 + sx + 3x + 3s
Comparing this with the given quadratic expression x^2 + rx + 12, we can equate the corresponding coefficients:
rx = sx + 3x
12 = 3s
Simplifying the first equation, we have:
rx - sx - 3x = 0
x(r - s - 3) = 0
Since this equation holds for all values of x, we can conclude that the expression in parentheses must be equal to zero:
r - s - 3 = 0
Now, we can substitute the value of s from the second equation into the above equation:
r - 12/3 - 3 = 0
r - 4 - 3 = 0
r - 7 = 0
Solving for r, we find:
r = 7
Therefore, the value of r is 7, which matches with option C.
We can expand the factored expression to get:
(x + 3)(x + s) = x^2 + sx + 3x + 3s
Comparing this with the given quadratic expression x^2 + rx + 12, we can equate the corresponding coefficients:
rx = sx + 3x
12 = 3s
Simplifying the first equation, we have:
rx - sx - 3x = 0
x(r - s - 3) = 0
Since this equation holds for all values of x, we can conclude that the expression in parentheses must be equal to zero:
r - s - 3 = 0
Now, we can substitute the value of s from the second equation into the above equation:
r - 12/3 - 3 = 0
r - 4 - 3 = 0
r - 7 = 0
Solving for r, we find:
r = 7
Therefore, the value of r is 7, which matches with option C.
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