Question

P(x)=4x-kx+9 can be written the product of two first degree polynomial.find the least value of k?

Answer 1

Given: P(x)=4x²-kx+9

To find: Find the least value of k?

Solution:

• As we have given that P(x) can be written as the product of two, first degree polynomial, so it means that determinant is equal to zero.

• So, lets calculate the determinant, we have

               P(x) = 4x² - kx + 9

• Formula for determinant is D = b² - 4ac

• So, determinant is equal to:

               (-k)² - (4 x 4 x 9) = 0

• As we can see that determinant include the term of k, so we can find the value of k,

• So:

               k² = 144

                k = 12 or k = -12  

• So, in one degree polynomial, we can write it as:

              so p(x)=4x²+12x+9=0, using k=-12

               4x²- (-12)x + 9 = 0

              (2x+3)² = 0

               x=-3/2

Answer:

             The least value of k is -12.