Question

x^2 + 5x - 7 = 0 has roots a and B.
find an equation whose roots are a^2 and B^2.

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Answer 1

→ Hey user,

→ Given Question:-

→ x² + 5x - 7 = 0 has roots α and β.find an equation whose

 roots are α² and β².

→ To find :-

→ Find an equation whose roots are α² and β²

→ Solution :-

→ α² + β² = ( α + β) ² - 2αβ

→              = ( -5 )² - 2 ( -7 )

→              = 25 + 14

→              = 39

→ α²β²      =  ( αβ )²

→              =   ( -7  )²

→              =   49

→ Now , ( x - α ) ( x - β ) = 0

→ x² - ( α + β ) x + αβ     = 0

→ α + β = -5

→ αβ     = -7

→ we want,

→ α² + β² and α²β²

→ x² - ( α² + β² ) x + α²β² = 0

→ x² -39 x + 49 = 0

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