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Euclid Sample Paper 2 · Q19

Paper 2Algebra

For real kk, consider

∣x2−4x+3∣=k∣x−2∣+32.|x^2-4x+3|=k|x-2|+\frac32.

For which values of kk does the equation have exactly six distinct real solutions?

Ak<−32k<-\frac32
B−32<k<−2-\frac32<k<-\sqrt2
C−2<k<0-\sqrt2<k<0
D−32≤k<−2-\frac32\leq k<-\sqrt2
E−32<k≤−2-\frac32<k\leq-\sqrt2
Fk>−2k>-\sqrt2

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