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The roots of the equation ax2 + x + b = 0 are equal if

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The roots of a quadratic equation px2 + qx + r = 0 are equal only when q2 = 4pr

Given equation,

ax2 + x + b = 0

By comparing the above equation with px2 + qx + r = 0, we get

p = a;

q = 1

r = b

Thus putting the values in q2 = 4pr, we get

1 = 4ab

⇒ ab = 1/4