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If the zeroes of a quadratic polynomial $a x 2 + b x + c$ are both positive, then a, b and c all have the ____ sign.

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Detailed Solution

If the zeroes of a quadratic polynomial

are both positive, then a, b and c all have the different sign.
Given quadratic polynomial is

a x 2 + b x + c

and the zeroes of the polynomial are both positive.
If

α

and

β

are three zeroes of a quadratic polynomial, then
Sum of zeroes =

α + β = \frac{- b}{a}

Product of zeroes =

αβ = \frac{c}{a}

Since,

α + β = \frac{- b}{a} < 0

\Rightarrow α + β = - ive

\Rightarrow

One of the zeroes is negative.
Therefore,

α

and

β

have different sign.

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