Multiple choice

If $a, b, c\in Q$, then roots of the equation $(b+c-2a)x^{2}+(c+a-2b)x+(a+b-2c)=0$ are

  1. rational

  2. non-real

  3. irrational

  4. equal
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of coefficients is (b+c-2a) + (c+a-2b) + (a+b-2c) = 0. If the sum of coefficients is zero, one root is 1, and the other root is c/a (constant term / leading coefficient). Since a, b, c are rational, the roots are rational.

AI explanation

The sum of the coefficients is (b+c minus 2a) plus (c+a minus 2b) plus (a+b minus 2c), which equals 0, meaning x equal to 1 is a root. Since a, b, and c are rational numbers and the product of the roots equals (a+b minus 2c) divided by (b+c minus 2a), the second root must also be rational. Therefore, both roots of the quadratic equation are rational.

Keep practicing — related questions