Question

Quadratic polynomial 2xsquare-3x+1 has zeros as alpha and beta. Now form a new quadratic polynomial whose zeros are 3alpha and 3beta

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Solution :-

If α and β are the zeros of 2x² - 3x + 1,

then α + β = - b/a

⇒ α + β = 3/2

and αβ = c/a

⇒ αβ = 1/2

New quadratic polynomial whose zeros are 3α and 3β is :-

= x² - (Sum of the roots)x + Product of the roots

= x² - (3α + 3β)x + 9αβ

= x² - 3(3/2)x + 9(1/2)

= x² - 9/2 x + 9/2

= 1/2 (2x² - 9x + 9)

Hence, the required quadratic polynomial is 1/2 (2x² - 9x +9).