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Official 2019 Paper 1 · Q2

Paper 1Algebra

Find the complete set of values of the real constant kk for which the expression

x2+kx+2x+1−2kx^2+kx+2x+1-2k

is positive for all real values of xx.

A−12<k<0-12<k<0
Bk<−12k<-12 or k>0k>0
C−6−3<k<6−3-\sqrt6-3<k<\sqrt6-3
Dk<−6−3k<-\sqrt6-3 or k>6−3k>\sqrt6-3
E−2<k<12-2<k<\frac12
Fk<−2k<-2 or k>12k>\frac12
G0<k<40<k<4
Hk<0k<0 or k>4k>4

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