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tmua.me Medium Set D Paper 1 · Q20

Paper 1Algebra

For a real number kk, the equations

x2+kx−2=0andx2+x+k2−3=0x^2+kx-2=0 \qquad\text{and}\qquad x^2+x+k^2-3=0

have exactly one common real solution.

What is the sum of all possible values of kk?

A−3-3
B−32-\dfrac32
C−12-\dfrac12
D11
E−3+174\dfrac{-3+\sqrt{17}}4

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