If the quadratic equation ax²-bx+12=0 where a and b are positive integers not exceeding 10, has roots both greater than 2. Then the number of possible ordered pair (a,b) is?

To determine the number of ordered pairs ( 𝑎 , 𝑏 ) (a,b) for the quadratic equation 𝑎 𝑥 2 − 𝑏 𝑥 + 12 = 0 ax 2 −bx+12=0 with roots both greater than 2, we first need to apply Vieta's formulas. The sum of the roots, given by 𝑏 𝑎 a b ​ , must be greater than 4, while the product of the roots, 12 𝑎 a 12 ​ , must also be greater than 4. This leads to the inequalities 𝑏 > 4 𝑎 b>4a and 𝑎 < 3 a<3. Considering the constraints that 𝑎 a and 𝑏 b are positive integers not exceeding 10, we can systematically explore valid combinations. Ultimately, by checking these conditions, we find the https://www.linkedin.com/pulse/best-dissertation-writing-services-top-websites-reviewed-gloria-kopp-qhukf feasible pairs that satisfy the criteria, leading to the conclusion of the possible combinations.

Posted by Arthur Swanson on 2024-09-21 04:13:22