Find a third-degree polynomial equation with rational coefficients that has the roots 2 and -3 + i. a. 0 = x^3 + 8x^2 + 22x + 20 b. 0 = x^3 + 4x^2 - 2x - 20 c. 0 = x^3 + 4x^2 + 22x - 20 d. 0 = x^3 - 4x^2 - 2x + 20

Option B

Step-by-step explanation:

Complex roots occur as conjugate pairs so the third root is -3 - i ( note that the sign changes from + to -).

So in factor form we have:-

(x - 2)(x - (-3 + i))(x - (-3 - i)) = 0    Let's expand the last 2 factors first:-

(x - (-3 + i))(x - (-3 - i))

= (x + 3 - i)(x + 3 + i)

= x^2 + 3x +ix + 3x + 9 + 3i - ix - 3i - i^2

= x^2 + 6x + 9 - (-1)

= x^2 + 6x + 10

Now multiplying by (x - 2):-

(x - 2)(x^2 + 6x + 10) = 0

x^3 + 6x^2 + 10x - 2x^2 - 12x - 20 = 0

x^3 + 4x^2 - 2x - 20 = 0    (answer)

Option B

plants store their excess carbohydrate in the form of starch so that it could be used as energy source later on. the excess carbohydrate is converted into starch in the plastid i.e. chloroplast & this process occurs in the presence of sunlight. it is an insoluble polymer of glucose which gets stored in cell organelles named as amyloplasts. in some plants, starch is also stored in roots and embryos.

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