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If α and β are the root of x2 + 32x + 200 then find the value of α/β + β/α.

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If α and β are the root of x2 + 32x + 200 then find the value of α/β + β/α.
1). 3.2
2). 1.2
3). 3.12
4). 4.32


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Answered by on | Votes 0 |

We have

x2 + 32x + 200

Sum of the root

(α + β) = -32

Product of the root

⇒ (αβ) = 200

Now,

α/β + β/α

⇒ (α2 + β2) /αβ

⇒ (α2 + β2 + 2αβ – 2αβ) /αβ

⇒ [(α + β)2 /αβ – (2αβ/αβ)]

⇒ (α + β)2 /αβ – 2

⇒ (-322/200) – 2

⇒ (1024/200) – 2

⇒ 5.12 – 2 = 3.12

∴ The value of α/β + β/α is 3.12

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