Question

Is the following statement true or false ? Justify your answer . if the zeroes of a quadratic polynomial ax2+bx+c are both negative , then a,b and c all have same sign

Answer 1

The given quadratic polynomial is ax2 + bx + c.

Let ∝ and β be the zero of the given quadratic polynomial.

Given, ∝ and β are both negative.

∴ ∝ + β is negative and ∝ β is positive.

is positive and

is positive.

⇒ a, b, c are all positive or a, b, c are all negative.

Hence, a, b and c all have same sign.