Question

find the value of k if (x-2) is a factor of p (x)=3x^3+4x^2-20x+k+2​

Answer 1

Answer :

k = -2

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

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Given polynomial,

p(x) = 3x³ + 4x² - 20x + k + 2

=> (x - 2) is a factor

   x - 2 = 0

   x = +2

Since (x - 2) is a factor,

substitute x = + 2 in the given polynomial, the result is zero.

p(2) = 0

3(2)³ + 4(2)² - 20(2) + k + 2 = 0

3(8) + 4(4) - 40 + k + 2 = 0

24 + 16 - 40 + k + 2 = 0

 40 - 40 + k + 2 = 0

  k + 2 = 0

    k = -2

∴ The value of k is -2