For the polynomial \(p(x)=x^2-12x+40\), at which value of \(x\) is the minimum value attained?
Answer and explanation
Correct answer: \(x=6\)
Completing the square gives \(p(x)=x^2-12x+40=(x-6)^2+4\). Since \((x-6)^2\geq 0\), its least value is 0 when \(x=6\). Therefore, the polynomial has minimum value 4 at \(x=6\). As an exam tip, writing a quadratic in the form \(a(x-h)^2+k\) immediately gives the vertex's x-coordinate as \(h\) when \(a>0\).
Frequently asked questions
What is the correct answer to this question?
\(x=6\)
Why is this the correct answer?
Completing the square gives \(p(x)=x^2-12x+40=(x-6)^2+4\). Since \((x-6)^2\geq 0\), its least value is 0 when \(x=6\). Therefore, the polynomial has minimum value 4 at \(x=6\). As an exam tip, writing a quadratic in the form \(a(x-h)^2+k\) immediately gives the vertex's x-coordinate as \(h\) when \(a>0\).
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.
