Let f(x)=x^2-2 p x+p^2-1 , where p R- -1,1 . If and are distinct real roots of the equation f(x)=0 such that | ^2+ ^2+3 | 5 , then set of values of p [a, b] . The value of [2 (a^2+b^2 ) ] is: [Note: [k] denotes greatest integer less than or

Question

Let f(x)=x^2-2 p x+p^2-1 , where p R- -1,1 . If and are distinct real roots of the equation f(x)=0 such that | ^2+ ^2+3 | 5 , then set of values of p [a, b] . The value of [2 (a^2+b^2 ) ] is: [Note: [k] denotes greatest integer less than or equal to k .]

Quantrex Academy · Accepted Answer

Correct answer: 2

aligned & x^2-2 p x+p^2-1=0 & x=p 1 & | ^2+ ^2 +3 | 5 -8 ^2+ ^2 2 -8 ^2+ ^2 2 -8 2 (p^2+1 ) p^2-1 2 & -4 p^2+1 p^2-1 1 -4 1+ 2 p^2-1 1 -5 2 p^2-1 < 0 & p^2-1 -2 5 p^2 3 5 p [- 3 5 , 3 5 ] [a, b] & [2 (a^2+b^2 ) ]=2 aligned

Let f(x)=x^2-2 p x+p^2-1 , where p R- -1,1 . If and are distinct real roots of the equation f(x)=0 such that | ^2+ ^2+3 | 5 , then set of values of p [a, b] . The value of [2 (a^2+b^2 ) ] is: [Note: [k] denotes greatest integer less than or equal to k .]

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