Question

If the zeros of the quadratic polynomial ax2+bx+c.c is not equal to zero are equal then..( which of the following is correct )
a) c and a have opposite sign b) c and b have opposite sign
c) c and a have same sign d) c and b have same sign

Answer 1

Explanation:

Roots are equal if discriminant ,

d= b²- 4ac =0

which is possible only if ' a ' and ' c ' have same signs.

So option C is correct

Answer 2

If the zeros of quadratic polynomial ax² + bx + c.c is not equal to zero are equal then c and a will have the same sign.

• The zeroes of the given quadratic polynomial ax2 + bx + c, c ≠ 0 are equal. If coefficient of x² and the constant term have same sign which is c and a have the same sign. While b which is the coefficient of x can be positive/negative but not zero.

• Example - x² - 4x +4 = 0

        (x +2)² = 0

         x = -2

• Given the quadratic polynomial ax² + bx + c, c ≠ 0 are equal, which means D = 0

        b² - 4ac = 0

        b² = 4ac

        ac = b²/4

        ac > 0