If alpha and beta are the zeroes of f(x) =x^2-4x+3 find the value of alpha^4beta^2
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f ( x ) = x² - 4x + 3
By Middle Term Factorisation
f ( x ) = x² - 3x - x + 3
f ( x ) = x ( x - 3 ) - 1 ( x - 3 )
f ( x ) = ( x - 1 ) ( x - 3 )
To find the zeroes, f ( x ) = 0
→ 0 = ( x - 1 ) ( x - 3 )
Using Zero Product Rule
→ x - 1 = 0 and x - 3 = 0
→ x = 1 and x = 3
Let the zeroes be α and β.
•°• α = 1, β = 3
Now,
α⁴β²
Putting values, we get
→ ( 1 )⁴ ( 3 )²
→ ( 1 ) ( 9 )
→ 9
Hence, the answer is 9.
By Middle Term Factorisation
f ( x ) = x² - 3x - x + 3
f ( x ) = x ( x - 3 ) - 1 ( x - 3 )
f ( x ) = ( x - 1 ) ( x - 3 )
To find the zeroes, f ( x ) = 0
→ 0 = ( x - 1 ) ( x - 3 )
Using Zero Product Rule
→ x - 1 = 0 and x - 3 = 0
→ x = 1 and x = 3
Let the zeroes be α and β.
•°• α = 1, β = 3
Now,
α⁴β²
Putting values, we get
→ ( 1 )⁴ ( 3 )²
→ ( 1 ) ( 9 )
→ 9
Hence, the answer is 9.
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