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Let α and β be their zeroes.
Given, α = 1 / β.
In this quadratic polynomial,
Coefficient of x² = ( a² + a )
Coefficient of x = 3
Constant term = 6a.
We know that,
Product of zeroes = constant term ÷ coefficient of x²
⇒ α × 1/α = 6a ÷ ( a² + a )
⇒ 1 = 6a ÷ a ( a + 1 )
⇒ 1 = 6 / ( a + 1 )
⇒ ( a + 1 ) = 6.
⇒ a = 6 - 1
∴ a = 5.
Given, α = 1 / β.
In this quadratic polynomial,
Coefficient of x² = ( a² + a )
Coefficient of x = 3
Constant term = 6a.
We know that,
Product of zeroes = constant term ÷ coefficient of x²
⇒ α × 1/α = 6a ÷ ( a² + a )
⇒ 1 = 6a ÷ a ( a + 1 )
⇒ 1 = 6 / ( a + 1 )
⇒ ( a + 1 ) = 6.
⇒ a = 6 - 1
∴ a = 5.
sleepoholic:
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