Answer : B
The system can reduce to one equation x2 - k = x. We get x2 - x - k = 0.
Since it has only one solution, discriminant equals 0.
Therefore, (-1)2 - 4(1)(-k) = 0 and we get k = -1/4.
Answer : E
The question is telling you that α,β are the roots of the equation 3x2 - hx - b = 0.
Therefore, α + β means the sum of roots which is h/3.
Answer : C
Similar to the last question, we know a,b are the roots of the equation x2 + 4x + 1 = 0.
Therefore, a + b = -4 and ab = 1.
Note that a2 + b2 = a2 + b2 + 2ab – 2ab = (a + b)2 – 2ab = (-4)2 - 2(1) = 14.
The key is to represent a2 + b2 in terms of a + b and ab.
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