Question

If α and ß are the zeroes of the polynomial 3x²-2x-6. Then the values of α²+ß ⁴ is​

Answer 1

Correct Question :

If α and β are the zeroes of the polynomial 3x²-2x-6. Then the values of α² + β² is ;

To Find :-

• The value of α² + β².

Solution :-

Given,

• α and β are the zeroes of the polynomial 3x²-2x-6.

On comparing with ax² + bx + c , We get ;

↪ a = 3 , b = -2 , c = -6

Given, α and β are the zeroes of the polynomial 3x²-2x-6.

↪ Sum of roots = -b/a

↪ α + β = -(-2)/3

↪ α + β = 2/3

↪ Product of roots = c/a

↪ αβ = -6/3

↪ αβ = -2

Now, we need to find the value of α² + β²;

↪ α² + β² = (α + β)² - 2αβ

[ Putting values ]

↪ α² + β² = (2/3)² - 2(-2)

↪ α² + β² = 4/9 + 4

↪ α² + β² = 4 + 36/9

↪ α² + β² = 40/9

Therefore,

The value of α² + β² is 40/9.