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The difference between the roots of the equation x 2 + ax +1=0 is less than 5 1/2 then set of all possible values of a is?

The difference between the roots of the equation


x2 + ax +1=0 is less than 51/2  then set of all possible values of


 a is?

Grade:12

1 Answers

piyush garg
9 Points
12 years ago

let roots of equation areX and Y

then sum of roots=-a

product of roots XY=1

given difference of roots <5^1/2

squaring on both the sides

(X-Y)^2<5

(x-y)^2=(x+y)^2-4XY

=a^2-4<5

(a^2-9)<0

(a-3)(a+3)<0

a=(-3,3)

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