Question

If the zeros of a quadratic polynomial ax2 +bx+c are both positive then a,b and c all have the same sign it's a question of true or false

Answer 1

Answer:

True

Step-by-step explanation:

Yes it is true

Hope it helps

Answer 2

Answer:

FALSE

Step-by-step explanation:

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 > 0Read more on Sarthaks.com - https://www.sarthaks.com/878258/if-the-zeroes-of-quadratic-polynomial-ax-bx-are-both-positive-then-and-all-have-the-same-sign

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.Read more on Sarthaks.com - https://www.sarthaks.com/878258/if-the-zeroes-of-quadratic-polynomial-ax-bx-are-both-positive-then-and-all-have-the-same-sign