Question

plzz help in explaining this ​

Answer 1

Answer:

Factor: x^2 - 1 = 0

=> x^2 = 1

=> x = 1 [Since square root of 1 is also 1]

Put the value of x in the given equation:

a(1)^4 + b(1)^3 + c(1)^2 + d(1) + e = 0

=> a + b + c + d + e = 0

[Since any power of 1 results in 1]

proved.

__________

Answer 2

Answer:

Step by step explanation:

To prove: a + c + e = b + d + = 0

Given that,

x² - 1 = 0

Thus, value of x = 1

x² - 1 is a factor of equation: ax⁴ + bx³ + cx² + dx + e = 0

Putting the value of x as 1 here,

=> a(1)⁴ + b(1)³ + c(1)² + d(1) + e = 0

=> a + b + c + d + e = 0

Thus,

We can say that,

a + c + e = 0 or b + d = 0

=> a + c + e = b + d

Hence, proved that a + c + e = b + d = 0.