Number of roots (part - 4)

Algebra Level 5

The equation x 2 + a ∣ x ∣ + 1 = 0 x^2 + a|x| + 1 = 0 has no real roots if , where a is parameter.

a = − 2 a = -2 a ≥ 0 a \geq 0 a < − 2 a < -2 ϕ \phi − 2 < a < 0 -2 < a < 0 a > − 2 a > -2

Akhil Bansal by Akhil Bansal , 22, India

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1 solution

Aryan Goyat
Nov 28, 2015

the equation will have no real root if the minimum value of quadratic is at x<0 --->a>0, and f(0)>0 but f(0)=1 also we find D<0 IS WHEN a belongs to(-2,2),taking union of it we get a>-2

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