A cubic function has just two x-intercepts, one at X =aand the other at x =6. Write down at least three possible equations with these intercepts:

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The cubic function has two x-intercepts, one at x = a and the other at x = 6.

Three possible equations with these intercepts are:

(x - a)^2(x - 6) = 0

=> (x^2 - 2ax + a^2)(x - 6)

=> x^3 - 2ax^2 + a^2x - 6x^2 + 12ax...

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The cubic function has two x-intercepts, one at x = a and the other at x = 6.

Three possible equations with these intercepts are:

(x - a)^2(x - 6) = 0

=> (x^2 - 2ax + a^2)(x - 6)

=> x^3 - 2ax^2 + a^2x - 6x^2 + 12ax - 6a^2 = 0

=> x^3 - x^2(2a + 6) + x(a^2 + 12a) - 6a^2 = 0

(x - 6)^2(x - a) = 0

=> (x^2 + 36 - 12x)(x - a) = 0

=> x^3 + 36x - 12x^2 - x^2a - 36a + 12ax = 0

=> x^3 - x^2(12 + a) + x(12a + 36) - 36a = 0

The third equation can be 3x^3 - x^2(36 + 3a) + x(36a + 108) - 108a = 0

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