If one root of x ^ 3 -3ax^2 - x + 6 = 0 is 1, then find the value of a. Also find its remaining root
Автор: @mathwithabbas
Загружено: 2026-02-20
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EXERCISE 20.6
1. Find the remaining two roots of the following cubic equations, when one root is given:
(1) 2x ^ 3 - x ^ 2 - 2x + 1 = 0 and x = 1
(ii) x ^ 3 - 4x ^ 2 + x + 6 = 0 and x = 3
(iii) x ^ 3 - 28x + 48 = 0 and x = 2
2. Find the remaining two roots of the following biquadratic equations, when its two roots are given:
(i) 12x ^ 4 - 8x ^ 3 - 7x ^ 2 + 2x + 1 = 0 and x = 1 - 1/2
(ii) x ^ 4 + 4x ^ 2 - 5 = 0 and x = 1 ,-1
(iii) x ^ 4 + 2x ^ 3 - 13x ^ 2 - 14x + 24 = 0 and x = 3 ,-4
3. Find the value of m and remaining two roots of the equation 2x ^ 3 - 3m * x ^ 2 + 9 = 0 if its one root is 3.
4. If one root of x ^ 3 - 3a * x ^ 2 - x + 6 = 0 is 1, then find the value of a. Also find its remaining roots.
5. Find the value of a and b, if two roots of the equation x ^ 4 - a * x ^ 2 + bx + 252 = 0 are 6 and -2, also find its remaining two roots.
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