If a, ß are the roots of the equation 2x^2 - 3x + 7 = 0 find value of following symmetric equation
Автор: @mathwithabbas
Загружено: 2026-02-13
Просмотров: 5
Описание:
1. If a,ẞ are the roots of a quadratic equation. Express the following symmetric functions in terms of alpha + beta and αβ.
(i) (alpha - beta) ^ 2
(ii) (alpha + beta) ^ 3
(iii) alpha ^ 2 * beta ^ - 1 + beta ^ 2 * alpha ^ - 1
(iv) alpha ^ 3 * beta + alpha * beta ^ 3
(v) 1/(a ^ 3) + 1/(beta ^ 3)
(vi) (1/a - 1/beta) ^ 2
2. If a,ẞ are the roots of the equation 2x ^ 2 - 3x + 7 = 0 find the value of following symmetric functions.
(i) (1/a + 1/beta) ^ 2
(ii) alpha/(beta ^ 2) + beta/(alpha ^ 2)
(iii) 1/(aa + 1) + 1/(a*beta + 1)
3. If a,ẞ are the roots of the equation p * x ^ 2 + qx + q = 0 p ne0, find the value of sqrt(alpha/beta) + sqrt(beta/alpha)
4. Represent symmetric equation alpha + beta = 8 graphically when a and ẞ are the root of a quadratic equation and also plot the graph.
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