Is the solution to this quadratic equation rational or irrational? Why?
2x^2+3x−10=0

A. Irrational, because the answer is a decimal that does not repeat or terminate.
B. Rational, because the answer is a fraction.
C. Rational, because the answer is a whole number.
D. Irrational, because there is no solution to this quadratic.

answer: i think it's a

step-by-step explanation:

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