Multiple choice

If p, q are real and p $\neq$ q, then the roots of the equation $(p - q)x^2 + 5 (p + q)x - 2(p - q) = 0$ are real and unequal

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For roots to be real and unequal, the discriminant D = b^2 - 4ac must be > 0. D = [5(p+q)]^2 - 4(p-q)(-2(p-q)) = 25(p+q)^2 + 8(p-q)^2. Since squares are non-negative and p != q, D > 0.

AI explanation

For the roots to be real and unequal, the discriminant b^2 - 4ac must be greater than zero. Substituting the coefficients gives [5(p + q)]^2 - 4(p - q)(-2(p - q)) > 0, which simplifies to 25(p + q)^2 + 8(p - q)^2 > 0. Since the sum of two squared terms multiplied by positive constants is always positive for real numbers where p does not equal q, the roots are indeed real and unequal; the statement is true.

Keep practicing — related questions