Question

If both p and q belong to the set ( 1,2,3,4), then how many equations of the px2 + qx + 1 = 0 will have roots?​

Answer 1

For quadratic equation to have real roots,

D ≥ 0

=> b^2 - 4a ≥ 0

=> b^2  ≥ 4a

For,

(1) a = 1, 4a = 4, b = 2, 3, 4 (3 equations)

(2) a = 2, 4a = 8, b = 3, 4 (2 equations)

(3) a = 3, 4a = 12, b = 4 (1 equation)

(4) a = 4, 4a = 16, b = 4 (1 equation)

Thus, total 7 equations are possible.

#BeBrainly

Answer 2

Answer:

solved

Step-by-step explanation:

q² ≥ 4p

i) p = 1 , 4p = 4 , {q }= {2,3,4} → 3 equation

ii)p = 2 , 4p = 8 , {q }= { 3,4 } → 2

iii)p = 3, 4p = 12 , {q }= { 4 } → 1

iV)p = 4 , 4p =16 , {q }= { 4} → 1

the number of equations = 7