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in Complex number and Quadratic equations by (52.7k points)

If p, q ∈ {1, 2, 3, 4}, the number of equations of the form px2 + qx + 1 = 0 having real roots is

(A) 15

(B)  9 

(C)  7 

(D)  8

1 Answer

+1 vote
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Best answer

Correct option (C) 7

px2 + qx + 1 = 0

D = q2 -  4p

We have to check for which pair of (h, k) discriminant is greater or equal to zero. 

q = 1, p = No value

q = 2, p = 1

q = 3, p = 1, 2

q = 4, p = 1, 2, 3, 4

So the number of pairs is equal to 7. 

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