SSC CGL 11 Aug 2017 Shift 1 Paper

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Question : 61 of 100

Marks: +1, -0

If α and β are roots of the equation

3x^2 -1 3 x + 14 = 0

, then what is the value

(α/ β) + (β / α) ?

$65/28$
$53/14$
9
$85/42$

Solution:

3x^2 -1 3 x + 14 = 0

On comparing

ax^2 + bx + c = 0

a =3, b = -13, c = 0

α+β =-b/a=13/3

...(i)

αβ=c/a=14/3

⇒

α-β=√{(α+β)^2-4αβ }

⇒

α-β=√{(13/3)^2-4× 14/4}

=

√{169/9-{56× 3}/9}

⇒

αβ=√{{169-168}/9}=√{1/9}

∴

α-β=1/3

...(ii)
On solving Eqs. (i) and (ii),

α=7/3,β=2

α/β+β/α=7/{3 × 2}+{2× 3}/7+7/6+6/7

={49+36}/42=85/42

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