Question: If (x) = x4 + 9x3 + 35x2 – x + 4, then (– 5 + 2 \(\sqr...

Question

If (x) = x⁴ + 9x³ + 35x² – x + 4, then (– 5 + 2 $\sqrt{- 4}$ ) is equal to –

Answer 1

Let, y = – 5 + 4i ⇒ y² + 10y + 41 = 0

∴ x) = x⁴ + 9x³ + 35x² – x + 4

= x² (x² + 10x + 41) – x(x² + 10x + 41) + 4(x² + 10x + 41) – 160

= – 160

∴ (– 5 + 4i) = – 160

Question: If (*x*) = *x*<sup>4</sup> + 9*x*<sup>3</sup> + 35*x*<sup>2</sup> – *x* + 4, then  (– 5 + 2 \(\sqr...