Please solve q 37 ?

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Answer 1 · 2018-06-03T06:25:26

The correct answer is #option (4)#

Let the quadratic equation be

#f(x)=(x-a)(x-b)-1#

Then,

#f(a)=-1# and #f(b)=-1#

Therefore,

#a# and #b# are not the roots of the equation.

#a, b in RR# and #b>a#

#f(x)=x^2-(a+b)x-1#

The coefficient of #x^2# is #>0#, this is a parabola that opens upwards.

The vertex form of the equation is

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

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

The minimum value is

#f(x)=-1-((a+b)/2)^2# when #x=(a+b)/2#

Therefore,

There are #2# roots when

#x in (-oo, a] uu [b, +oo)#

The correct answer is #option (4)#