The number of real values of x that satisfies the equation x 4 + 4 x 3 + 12 x 2 + 7 x - 3 = 0 is

Question

The number of real values of x that satisfies the equation x 4 + 4 x 3 + 12 x 2 + 7 x - 3 = 0 is,

MARKS App · Accepted Answer

Let, f x = x 4 + 4 x 3 + 12 x 2 + 7 x - 3 ∴ f ′ x = 4 x 3 + 12 x 2 + 24 x + 7 f ″ x = 12 x 2 + 2 x + 2 i.e. f '' x > 0 , ∀ x ∈ R Also, f 0 = - 3 Hence, f x = 0 has 2 real roots

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