If the zeroes of the quadratic polynomial ax² + bx + c (c ≠ 0) are equal, then find the correct statement

Video Explanation

Watch the video explanation below:

Given

Quadratic polynomial: f(x) = ax² + bx + c,   c ≠ 0

The zeroes of the polynomial are equal.

To Find

The correct relationship between the coefficients.

Solution

Step 1: Condition for Equal Zeroes

For a quadratic polynomial ax² + bx + c, the zeroes are equal if:

b² − 4ac = 0

Step 2: Rearrange the Condition

b² = 4ac

Since b² is always positive or zero,

the product ac must be positive.

Step 3: Analyse the Sign of a and c

If ac is positive, then:

• a and c have the same sign

Given that c ≠ 0, this condition is valid.

Final Answer

The correct statement is:

c and a have the same sign

Correct Option

(c) c and a have the same sign

Conclusion

Hence, if the zeroes of the quadratic polynomial ax² + bx + c (c ≠ 0) are equal, then the coefficients a and c must have the same sign.