smc-750-30-Discriminant

Functions, MET2 2023 VCAA 19 MC

Find all the values of , such that the equation has two real solutions for , one positive and one negative.

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♦♦ Mean mark 32%.
MARKER’S COMMENT: 27% incorrectly chose A.

The set of values of for which has two real solutions is

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The equation has no real roots when

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♦♦ Mean mark 32%.

The graph of intersects the graph of at two distinct points for

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The graphs of and will have no points of intersection for all values of and such that

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♦ Mean mark 37%.

The graph of intersects the graph of at two distinct points for

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The cubic function , where and are positive constants, has no stationary points when

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♦♦ Mean mark 29%.