For a given k, what is the minimum value of \( x^2 + kx + k^2 \) ?
- A. 0
- B. \( \frac{k^2}{4} \)
- C. \( \frac{3k^2}{4} \) ✓
- D. \( \frac{k^2}{2} \)
Correct Answer: C. \( \frac{3k^2}{4} \)
Explanation
The minimum value of a quadratic expression \( ax^2 + bx + c \) is \( \frac{4ac - b^2}{4a} \). Substituting a=1, b=k, c=k^2 gives \( \frac{4k^2 - k^2}{4} = \frac{3k^2}{4} \).
Related questions on Algebra
- How many four-digit natural numbers are there such that <strong>ALL</strong> of the digits are odd?
- What is \sum_{r=0}^{n}2^{r}C(n,r) equal to ?
- If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) a...
- Consider the following statements : 1. If f is the subset of Z\times Z defined by f=\{(xy,x-y);x,y\in Z\}, then f is a function from...
- For how many quadratic equations, the sum of roots is equal to the product of roots?