Question

alpha, beta, gamma, sigma are the roots of equation x +4x³-6x²+7x-9-0, the value of π(1+ a²) is​

Answer 1

Answer:

13

Step-by-step explanation:

x4 + 4x3 – 6x2 + 7x – 9 = (x - α)(x - β)(x - γ)(x - δ) Put x = i, i4 + 4i3 – 6i2 + 7i – 9 = (i- α)(i - β)(i - γ)(i - δ) –2 + 3i = (i- α)(i - β)(i - γ)(i - δ) ...(1) Put x = – i – 2 – 3i = (-i- α)(-i - β)(-i - γ)(-i - δ) ....(2) Multiply (1) & (2) 4–9i2 = (α2 + i2)(β2 + i2)(γ2 - i2)(δ2 - i2) 13 = (1 + α2)(1+ β2)(1 + γ2)(1 + δ2)Read more on Sarthaks.com - https://www.sarthaks.com/485203/if-are-roots-of-x-4-4x-3-6x-2-7x-9-0-then-the-value-of-1-2-1-2-1-2-1-2-is