Question

If alpha and beta are the zeros of ax^2+bx+c.then evaluate alpha raised 4
beta raised 4

Answer 1

Answer :

  α⁴ + β⁴ = (b⁴ - 4b²ca+2c²a²)/a⁴

Solution :

The given polynomial is

  P(x) = ax² + bx + c

Since α and β are the zeroes of P(x), by the relation between zeroes and coefficients, we get

    α + β = - b/a .....(i)

    αβ = c/a .....(ii)

Now, α⁴ + β⁴

= (α² + β²)² - 2α²β²

= {(α + β)² - 2αβ}² - 2 (αβ)²

= {(- b/a)² - 2 (c/a)}² - 2 (c/a)²

= (b²/a² - 2c/a)² - 2c²/a²

= {(b² - 2ca)/a²}² - 2c²/a²

= (b⁴ - 4b²ca + 4c²a²)/a⁴ - 2c²/a²

= (b⁴ - 4b²ca + 4c²a² - 2c²a²)/a⁴

= (b⁴ - 4b²ca + 2c²a²)/a⁴

Answer 2

Step-by-step explanation:

This is the Proper Solution for the Given Question .

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