Question

Write a cubic polynomial whose zeroes are -2,5, -7.
fully solved
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Answer 1

Given :   a cubic polynomial whose zeroes are -2,5, -7.

To Find :  cubic polynomial

Solution:

cubic polynomial whose zeroes are -2,5, -7.

cubic polynomial = (x - (-2))(x - 5)(x -(-7))

= (x + 2)(x - 5)(x + 7)

= (x - 5)(x + 2)(x + 7)

= (x - 5)(x² + 9x + 14)

= x³ + 9x²  + 14x  - 5x² - 45x - 70

= x³ + 4x² - 31x - 70  

cubic polynomial  is x³ - 4x² - 31x - 70  

Another method

Sum of zeroes = -2 + 5 - 7  = - 4

Product of zeroes taking 2 together = -10 + 14 - 35 =  -31

Product of zeroes = 70

x³ -(-4)x² + (-31)x -(70)

= x³ + 4x² - 31x - 70

x³ - 4x² - 31x - 70  is a cubic polynomial whose zeroes are -2,5, -7.

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