Question

The value of a for which (x-3) is a factor of x power 3 +x power 2 _ 17 x+a is
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Answer 1

Answer :

a = 15

Step-by-step explanation :

⇒ Cubic Polynomial :

• It is a polynomial of degree 3.

• General form :

     ax³ + bx² + cx + d

• Relationship between zeroes and coefficients :

      ☆ Sum of zeroes = -b/a

      ☆ Sum of the product of zeroes taken two at a time = c/a

      ☆ Product of zeroes = -d/a

_______________________________

Given cubic polynomial,

x³ + x² - 17x + a

=> (x - 3) is a factor

     x - 3 = 0

       x = +3

Substitute x = 3, the result is zero since (x - 3) is a factor.

  x³ + x² - 17x + a = 0

  3³ + 3² - 17(3) + a = 0

  27 + 9 - 51 + a = 0

    36 - 51 + a = 0

       - 15 + a = 0

            a = 15

∴ The value of a is 15.