Part BCSIR NET June 2024cross-terms-do-not-imply-indefinite

Cross terms do not imply indefinite

For a quadratic form $f (x, y, z) \in R [x, y, z]$ , we say that $(a, b, c) \in R^{3}$ is a zero of f if f(a, b, c) = 0. Which of the following quadratic forms has at least one zero different from (0, 0, 0)?

A. $x^{2} + 2 y^{2} + 3 z^{2}$
B. $x^{2} + 2 y^{2} + 3 z^{2} - 2$ xy
C. $x^{2} + 2 y^{2} + 3 z^{2} - 2$ xy − 2yz
D. $x^{2} + 2 y^{2} - 3 z^{2}$ ✓

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Cross terms do not imply indefinite

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