If the zeroes of the quadratic polynomial ax² + bx + c, where c≠0, are equal, then

Question

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

Philoid · Accepted Answer

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

i.e. D = 0

b² - 4ac = 0

4ac = b²

ac = b²/4 > 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

If the zeroes of the quadratic polynomial ax2 + bx + c, where c≠0, are equal, then