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
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 3.123. IF $a^{2}+ab^{2}+c^{2}$= 83 and a + b + c = 15 then the value of ab + bc + ca is
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