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If one root of 5x2 + 26x + k = 0 is reciprocal of the other, then what is the value of k?
1. 2
2. 3
3. 5
4. 8

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Correct Answer - Option 3 : 5

Concept: 

Let us consider the standard form of a quadratic equation, ax2 + bx + c =0

Let α and β be the two roots of the above quadratic equation. 

The sum of the roots is given by:  \({\rm{α }} + {\rm{β }} = - \frac{{\rm{b}}}{{\rm{a}}} = - \frac{{{\rm{coefficient\;of\;x}}}}{{{\rm{coefficient\;of\;}}{{\rm{x}}^2}}}\) 

The product of the roots is given by:  \({\rm{α β }} = \frac{{\rm{c}}}{{\rm{a}}} = \frac{{{\rm{constant\;term}}}}{{{\rm{coefficient\;of\;}}{{\rm{x}}^2}}}\)

 

Calculation:

Let the roots of 5x2 + 26x + k = 0 are α and β

Given α = 1/β 

⇒ α.β = 1    ----(i)

Compare with general equation ax2 + bx + c = 0

a = 5, b = 26, c = k

According to the concept used

⇒ α.β = k/5    ----(ii)

From (i) and (ii), we get 

k/5 = 1

∴The value of k is 5.

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