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The α and β are the roots of the equation Ax2 – 7x + 6 = 0 and the 1/α and 1/β are the roots of the equation  6x2 – 7x + 2 = 0, then, what is the value of A?

The α and β are the roots of the equation Ax2 – 7x + 6 = 0 and the 1/α and 1/β are the roots of the equation  6x2 – 7x + 2 = 0, then, what is the value of A? Correct Answer 2

Given:

The α and β are the roots of the equation Ax2 – 7x + 6 = 0

The 1/α and 1/β are the roots of the equation 6x2 – 7x + 2 = 0

Concept Used:

x2 - ( sum of the roots) x + product of the roots = 0

Calculation:

Ax2 – 7x + 6 = 0

⇒ (α + β) = 7/A

&, αβ = 6/A

6x2 – 7x + 2 = 0

⇒ (1/α + 1/β) = 7/6

&, 1/αβ = 2/6

Therefore, 1/(6/A) = 2/6

⇒ A/6 = 2/6

⇒ A = 2

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