If the minimum value of \(p(x)=x^2-2x+k\) is \(3\), what is the value of \(k\)?
Answer and explanation
Correct answer: 4
Completing the square gives \(p(x)=x^2-2x+k=(x-1)^2+k-1\). Since \((x-1)^2\geq 0\), the minimum value occurs at \(x=1\) and is \(k-1\). Therefore, \(k-1=3\), so \(k=4\). Exam tip: rewrite a quadratic as a square plus a constant to identify its minimum or maximum value quickly.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Completing the square gives \(p(x)=x^2-2x+k=(x-1)^2+k-1\). Since \((x-1)^2\geq 0\), the minimum value occurs at \(x=1\) and is \(k-1\). Therefore, \(k-1=3\), so \(k=4\). Exam tip: rewrite a quadratic as a square plus a constant to identify its minimum or maximum value quickly.
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.
