Multiple choice

If $l, m, n$ are real, $l\neq m$, then the roots of the equation $(l-m)x^2-5(l+m)x-2(l-m)=0$ are

  1. real and equal

  2. complex

  3. real and unequal

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The discriminant is 25(l + m)^2 + 8(l - m)^2. Because l and m are real and l != m, the second term is positive, so the discriminant is positive and the roots are real and unequal.

AI explanation

To determine the nature of the roots, we evaluate the discriminant D = B^2 - 4AC for the given equation. Substituting A = (l-m), B = -5(l+m), and C = -2(l-m), we get D = (-5(l+m))^2 - 4(l-m)(-2(l-m)), which simplifies to D = 25(l+m)^2 + 8(l-m)^2. Since l and m are real numbers with l not equal to m, both terms in the sum are positive, meaning D is always strictly greater than zero. Therefore, the roots of the quadratic equation are real and unequal.

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