Multiple choice

Say true or false: If the zeroes of a quadratic polynomial $ax^2 + bx + c$ are both positive, then $a, b$ and $c$ do not have the same sign.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If the roots are positive, their sum (-b/a) must be positive and their product (c/a) must be positive. If c/a > 0, then a and c have the same sign. If -b/a > 0, then a and b must have opposite signs. Thus, a, b, and c cannot all have the same sign.

AI explanation

If the zeroes of a quadratic polynomial ax^2 + bx + c are both positive, their sum (-b/a) is positive and their product (c/a) is positive. This implies that b and a must have opposite signs, while c and a must have the same sign. Therefore, a, b and c can never all have the same sign, making the statement true.

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