If \(P(x)=x^2+px+q\), \(P(0)=12\), and \(P(3)=0\), what is the value of the coefficient \(p\)?
Answer and explanation
Correct answer: -7
Since \(P(0)=q=12\), substituting \(x=3\) in \(P(x)=x^2+px+q\) gives \(9+3p+12=0\). Thus, \(3p=-21\) and \(p=-7\), so option A is correct. Exam tip: use the value at \(x=0\) first to determine the constant term, then substitute the second given value to find the unknown coefficient.
Frequently asked questions
What is the correct answer to this question?
-7
Why is this the correct answer?
Since \(P(0)=q=12\), substituting \(x=3\) in \(P(x)=x^2+px+q\) gives \(9+3p+12=0\). Thus, \(3p=-21\) and \(p=-7\), so option A is correct. Exam tip: use the value at \(x=0\) first to determine the constant term, then substitute the second given value to find the unknown coefficient.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
