If the zeroes of the quadratic polynomial ax^{2} + bx + c, where c≠0, are equal, then

the zeroes of a quadratic polynomial are equal when discriminate is equal to 0

i.e. D = 0

b^{2} - 4ac = 0

4ac = b^{2}

ac = b^{2}/4 > 0 (square of any positive or negative number is positive )

ac > 0

For ac > 0, a and c must have the same sign

i.e., either a > 0 and c > 0 or a < 0 and c < 0

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