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Find a positive value of p if the expression 2x² – px + p leaves a…
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Find a positive value of p if the expression 2x² – px + p leaves a remainder 6 when divided by x – p
A. 4
B. 3
C. 2
D. 1
QUICK ANSWER…
C
DETAILS…
Pay close attention and follow these steps to resolve questions like this.
- Equate the divisor to zero, and make x the subject of the formula like this: x – p = 0, x = p
- Substitute x for p in the main expression like this: 2x² – px + p = 2(p)² – p(p) + p = 2p² – p² + p = p² + p
- Finally, equate the answer to the remainder like this: p² + p = 6
Solving this, we have:
p² + p = 6
p² + p – 6 = 0
factorizing, we have:
p² – 2p + 3p – 6 = 0
(p² – 2p) + (3p – 6) = 0
p(p – 2) + 3(p – 2) = 0
(p – 2)(p + 3) = 0
Therefore,
P – 2 = 0, p = 2
Or p + 3 = 0, p = -3
So, p = 2 or -3
Taking the positive value as required by the question, we have p = 2
Now for the right answer to the above question:
- Option A is incorrect.
- Option B is incorrect.
- C is correct.
- D is not the correct answer.
KEY-POINTS…
You may please note these/this:
- The steps are clear…
- Firstly, make x the subject of the divisor.
- Secondly, substitute x for p into the original expression.
- Thirdly, we will be left with an equation containing only p, then solve to find p.
- Take the positive value of p as the required answer.
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/ culled from 2020 JAMB-UTME mathematics past question 33 /
