JEE Main202228 Jun 2022Morning ShiftMathematicsApplication of DerivativesActual

The number of real solutions of x 7 + 5 x 3 + 3 x + 1 = 0 is equal to _____.

Options

Correct answer

B. 1

Step-by-step solution

f x = x 7 + 5 x 3 + 3 x + 1 For number of real solutions, we need to find the number of times the curve cuts x - axis. Now f ' x = 7 x 6 + 15 x 2 + 3 > 0 ∴     f x is strictly increasing function i.e. when x → - ∞ , y → - ∞ and when x → ∞ , y → ∞ So, the curve will cut x - axis only once. ∴ number of real solution will be 1

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