Let p be the product and s be the sum of non-real roots of the equation x4 – 4x3 + 6x2

Engineering

Mathematics

Leibnitz Rule Derivative of Anti Derivatives

Question

Let p be the product and s be the sum of non-real roots of the equation x⁴ – 4x³ + 6x² – 4x = 48, then

s + p = 10

Number of roots of the equation $\cos^{- 1} (\frac{1 - x^{2}}{1 + x^{2}})$ = p – 3s is 2.

$\underset{x \to 0^{+}}{Lim} \frac{\int_{1}^{\cos (sx)} (\cos^{- 1} t) dt}{sx - \sin (sx)}$ equals – 2.

s³ – p – 2 = 0

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x⁴ – 4x³ + 6x² – 4x + 1 = 48 + 1
(x – 1)⁴ = 49 ⇒ (x – 1)² = – 7 for non real roots
x² – 2x + 8 = 0
$∴$ s = 2 and p = 8
Now verify.