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Grade 11Algebra

For what values of a belongs to R, do the roots of x²-2x-(a²-1)=0, lie between the roots of x²-2(a+1)x+a(a-1)=0,
Could you pls assist me with detailed step by step solution.

Surya

8 Years agoGrade 11

1 Answer

Surya

8 Years ago

f(x)=0

=x²-2x-(a²-1)=0

=(x-1)²-a²=0

So, x=1 $\pm$ a

Let $\alpha$ =1-a and Let $\beta$ =1+a

Now lets Consider 3 cases:

1) $\Delta$ $>$ 0= a $\in$ (-1/3,Infinity)----(i)

2)g( $\alpha$ ) $<$ 0=a $\in$ (-1/4,1)------(ii)

3)g( $\beta$ ) $<$ 0=a $\in$ (-1/3, Infinity)---------(iii)

Now taking intersection of all three cases, we get,

a $\in$ (-1/4,1)

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