Question

Assertion (A): If the zeros of the quadratic polynomial $$ax^{2}+bx+c$$ are both negative then a, b, c will have the same sign.

Reason (R): The zeros of a quadratic polynomial are either both positive or both negative.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is true and Reason (R) is false.

Explanation:

Step 1 – Assertion: A is true. If the negative zeros are $$\alpha$$ and $$\beta$$, then $$\alpha+\beta<0$$ and $$\alpha\beta>0$$. Since $$\alpha+\beta=-\frac{b}{a}$$ and $$\alpha\beta=\frac{c}{a}$$, the coefficients $$a,b,c$$ have the same sign.

Step 2 – Reason: R is false. The zeros of a quadratic polynomial need not both have the same sign; for example, a quadratic may have one positive and one negative zero.