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Question
If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign.
Options
True
False
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Solution
This statement is False.
Explanation:
If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then
α + β = `- b/a` and αβ = `c/a`
Where α and β are the zeroes of the quadratic polynomial and α, β > 0.
∴ c < 0, a < 0 and b > 0
or c > 0, a > 0 and b < 0
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