When 2x^2+x+c is divided by x+k, the quotient is 2x+5 and the remainder is 7. Find c and k. a. k = 1, c = -3

b. k = -5, c = -6

c. k = 2, c = 3

d. k = -2, c = -3

the answer is b

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0