If a, b and c are real numbers, such that a + 2b + 4c = 0. Then, the equation ax2 + bx + c = 0

1) has both the roots complex

2) has its roots lying within – 1 < x < 0

3) has one of the roots equal to 1/2

4) has its roots lying within 2 < x < 6

Solution: (3) has one of the roots equal to 1/2

a + 2b + 4c = 0

(1 / 4) a + (1 / 2) b + c = 0

(1 / 2)2 a + (1 / 2) b + c = 0

On comparing with ax2 + bx + c = 0,

x = 1 / 2

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