Find the value of the constant k such that (x–1) is a factor of 2x^2+9x^2+kx–5. With this value for k solve the equation 2x^3+9x^2+kx–5=0.

Answer 1

divide , using long division, (x-1) into 2x^3+9x^2+kx-5

the quotient will be 2x^2 +11x +k+11

the remainder will be k+6

the remainder must equal 0 so k+6=0 and k=-6

the quotient becomes 2x^2+11x+5

2x^2+11x+5=0

(2x+1)(x+5)=0

2x+1=0 and x=-1/2

x+5=0 and x=-5

also, x=1 is the third solution