Trigonometric EquationMedium
Question
The integral values of ′a′ for which the equation cos2x - (a2 + a + 5)|cos x| + (a3 + 3a2 + 2a + 6) = 0 hasatleast one real solution, are -
Options
A.- 3
B.- 2
C.- 1
D.0
Solution
Let α, β be the roots of the equation then
α + β = (a2 + a + 5)
α, β = (a2 + 2)(a + 3)
⇒ 0 ≤ (a2 + 2) ≤ 1
⇒ 0 ≤ (a + 3) ≤ 1
⇒ a = -3, -2
α + β = (a2 + a + 5)
α, β = (a2 + 2)(a + 3)
⇒ 0 ≤ (a2 + 2) ≤ 1
⇒ 0 ≤ (a + 3) ≤ 1
⇒ a = -3, -2
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