Question

If alpha nd beta are the zeros of polynomial 9 x square + 9x + 2 then find alpha square + beta square...

Answer 1

Answer:

Alpha square = 91x⁴

Beta square =4

Answer 2

Answer: g(x) = 9x² - 85x + 36

Explanation:

The given polynomial is f(x) = 3x² - 7x - 6

Since α and β are the zeroes of f(x),

    α + β = - (- 7/3)

⇒ α + β = 7/3 .....(i)

    αβ = - 6/3

⇒ αβ = - 2 .....(ii)

We need to find the polynomial whose roots are α² and β²

    Now, α² + β²

    = (α + β)² - 2αβ

    = (7/3)² - 2 (- 2)

    = 49/9 + 4

    = (49 + 36)/9

    = 85/9

⇒ α² + β² = 85/9

    α²β² = (- 2)²

⇒ α²β² = 4

The polynomial having zeroes α² and β² be

    g(x) = (x - α²) (x - β²)

    = x² - (α² + β²) x + α²β²

    = x² - (85/9) x + 4

    = (9x² - 85x + 36)/9

Hence, the required polynomial be

    g(x) = 9x² - 85x + 36