Answer :

If the zeroes of a quadratic polynomial ax2 + bx + c are both positive, then a, b and c all have the same sign: False.

Let α, β be the zeroes of the polynomial p(x) = ax2 + bx + c


Sum of the zeroes = - (coefficient of x) ÷ coefficient of x2


α + β = - b/a > 0 ( α > 0, β > 0 α + β > 0)


for – b/a > 0, b and a must have opposite signs.


Product of the zeroes = constant term ÷ coefficient of x2


αβ = c/a > 0 ( α,β > 0 αβ > 0)


for c/a > 0, c and a must have same signs.


Case 1: when a > 0


- b > 0 and c > 0


= b < 0 and c > 0


Case 2: when a < 0


- b < 0 and c < 0


= b > 0 and c < 0


Hence, the coefficients have different signs.


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