Question

If α, β are the zeroes of the polynomial 2x² - 3x + 7 then find α² + β²

Answer 1

❍ Given that, α, β are the zeroes of the polynomial 2x² - 3x + 7.

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To calculate the α² + β² we must know  that ::

• Sum of the zeroes of the quadratic equation -  

            α + β = -b/a

•  Products of the zeroes of the quadratic equation.  

            αβ = c/a

Finding  α² + β² :-

Identity : ( a² + b² ) = ( a + b )² - 2ab

⇒ α² + β² = (α + β)² - 2αβ.

Here,

α + β = - ( -3 )/2 = 3/2  

αβ = 7/2

[  By above information ]

⤳ α² + β² = (3/2)² - 2(7/2).

⤳ α² + β² = 9/4 - 7

⤳ α² + β² = (9 - 28)/7

⤳ α² + β² = - 19/7

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Henceforth, value of α² + β² is -19/7

Answer 2

Answer:

your answer is in the attachment