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Q1. From a cubic polynomial whose zeroes are 3, 2, and -1 . Hence find


a) sum of its zeros


b) sum of the product, taken two at a time.


c) Product of its zeroes.



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Answer 1

Answer: P(x)  = (x³ - 4x² + x + 6)

Step-by-step explanation:

Let, the zeroes be α , β , γ

α  = 3

β  = 2

γ  = -1

Polynomial Having  zeroes 3,2,-1 ,

P(x)  = (x - α)(x - β)(x - γ)

P(x)  = (x - 3)(x - 2)(x + 1)

P(x)  = (x² - 3x - 2x + 6)(x + 1)

P(x)  = (x² -5x + 6)(x + 1)

P(x)  = (x³ + x² - 5x² - 5x + 6x + 6)

P(x)  = (x³ - 4x² + x + 6)

Comparing this polynomial with standard form of  polynomial,

ax³ + bx² +cx +d, We  get

a = 1

b = -4

c = 1

d = 6

Sum of  zeros = -b/a = -(-4/1) = 4

Sum of the  product, taken two at a time = c/a = 1/1 = 1

Prodcut  of  its zeroes = -d/a = -6/1 = -6