If p(x) = 2x² − 5x + c and p(4) = 7, what is the value of c?
Answer and explanation
Correct answer: −5
The governing idea is evaluation of a polynomial: substitute the given input into p(x) and equate the result to the stated value. Since p(4) = 7, substitute x = 4 in 2x² − 5x + c: p(4) = 2(4)² − 5(4) + c = 2(16) − 20 + c = 32 − 20 + c = 12 + c. Therefore, 12 + c = 7, so c = 7 − 12 = −5. Thus option A is correct. Option B would result from an arithmetic error, while the positive answers ignore the fact that the constant must reduce 12 to 7.
Frequently asked questions
What is the correct answer to this question?
−5
Why is this the correct answer?
The governing idea is evaluation of a polynomial: substitute the given input into p(x) and equate the result to the stated value. Since p(4) = 7, substitute x = 4 in 2x² − 5x + c: p(4) = 2(4)² − 5(4) + c = 2(16) − 20 + c = 32 − 20 + c = 12 + c. Therefore, 12 + c = 7, so c = 7 − 12 = −5. Thus option A is correct. Option B would result from an arithmetic error, while the positive answers ignore the fact that the constant must reduce 12 to 7.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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