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Clavis TMUA Set A Paper 2 · Q16

Paper 2Logic & proof

Consider the following statement (∗)(*) about a real number xx:

(∗)(*) There exists a real number yy such that y2+xy+x=0y^2+xy+x=0.

What is the complete set of values of xx for which (∗)(*) is true?

Ax≤0x\leq0 or x≥4x\geq4
B0≤x≤40\leq x\leq4
Cx<0x<0 or x>4x>4
D0<x<40<x<4
Eall real values of xx
Fthere are no such values of xx

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