Mathsonfire said:86
tkhunny said:Those are nice problems. If you're prepping for the Olympiad, you will need the skills. If all else fails, brute force it! Of course, if you're not fast enough, you'll waste too much time.
Personally, I wrote down the ratios and solved for b. You could solve for any of the 4 remaining arbitrary coefficients.
They were nice to you and made them both monic quadratics.
Mathsonfire said:I didnt get it
The ratio of quadratic roots refers to the relationship between the two solutions of a quadratic equation. It is the ratio of the larger root to the smaller root.
To calculate the ratio of quadratic roots, first find the solutions of the quadratic equation by using the quadratic formula or factoring. Then, divide the larger root by the smaller root to find the ratio.
The ratio of quadratic roots can provide information about the nature of the solutions of a quadratic equation. For example, if the ratio is 1, it means that the two solutions are equal, indicating a perfect square trinomial. If the ratio is less than 1, it means that the solutions are real and unequal. If the ratio is greater than 1, it means that the solutions are complex conjugates.
No, the ratio of quadratic roots cannot be negative. It is always a positive value because the larger root is divided by the smaller root, resulting in a positive ratio.
The leading coefficient, or the coefficient of the squared term, affects the ratio of quadratic roots by determining the direction of the parabola. A positive leading coefficient results in a concave up parabola and a ratio greater than 1, while a negative leading coefficient results in a concave down parabola and a ratio less than 1.