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<h2>The greatest possible value of the second root, β = 54 </h2>
Step-by-step explanation:
The given quadratic equation:
Let α and β be the roots of the given quadratic equation.
α = 36
To find, the greatest possible value of the second root ( β) = ?
∴ The sum of the roots,
α + β =
⇒ 36 + β =
⇒ 5m = 36 + β ............. (1)
The product of the roots,
α.β =
⇒
⇒ ............. (2)
From equations (1) and (2), we get
⇒
⇒
⇒
⇒ β(β - 54) - 24(β - 54) = 0
⇒ (β - 54)(β - 24) = 0
⇒ β - 54 = 0 or, β - 24 = 0
⇒ β = 54 or, β = 24
∴ The greatest possible value of the second root, β = 54