If the difference between the roots of the equation x 2 + a x + 1 = 0 is less than 5 , then the set of possible values of a is

Question

If the difference between the roots of the equation x 2 + a x + 1 = 0 is less than 5 ​ , then the set of possible values of a is

TestHub · Accepted Answer

x 2 + a x + 1 = 0 α + β = − a α β = 1 ∣ α − β ∣ = ( α + β ) 2 − 4 α β ​ ∣ α − β ∣ = a 2 − 4 ​ a 2 − 4 ​ < 5 ​ a 2 − 4 < 5 a 2 − 9 < 0 a ∈ ( − 3 , 3 ) .

Mathematics - Quadratic Equation Question with Solution | TestHub

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