Please solve q 38 ?

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Answer 1 · 2018-06-02T18:24:47

The answer is #option (2)#

An identity is

#(x+c)^2=x^2+2cx+c^2#

Here,

The equation is

#(a^2-3a+2)x^2+(a^2-4)x+(a^2-a-2)=0#

#(a-2)(a-1)x^2+(a+2)(a-2)x+(a-2)(a+1)=0#

Dividing by #(a-2)(a-1)#

#x^2+(a+2)/(a-1)x+(a+1)/(a-1)=0#

Therefore,

#2c=(a+2)/(a-1)# and #c^2=(a+1)/(a-1)#

Eliminating #c#

#1/4*(a+2)^2/(a-1)^2=(a+1)/(a-1)#

#(a+2)^2=4(a+1)(a-1)#

#a^2+4a+4=4a^2-4#

#3a^2-4a-8=0#

The discriminant is

#Delta=b^2-4ac=16+96=112#

As #Delta>0#, there are #2# real solutions.

The answer is #option (2)#