Multiple choice

If the quadratic equation $\displaystyle x^{2}-mx-4x+1=0$ has real and distinct roots, then the values of $m$ are A. $\displaystyle (-\infty , -6)$ B. $\displaystyle (-\infty,-3)$ C. $(-2,\infty )$ D. $\displaystyle \left ( 2,\infty \right )$

  1. A or C

  2. A or D

  3. B or C

  4. B or D
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Equation: x^2 - (m+4)x + 1 = 0. For real and distinct roots, discriminant D > 0. D = (m+4)^2 - 4 > 0. (m+4)^2 > 4. So m+4 > 2 or m+4 < -2. This means m > -2 or m < -6.

AI explanation

Rewrite the equation as x^2 - (m + 4)x + 1 = 0. For the roots to be real and distinct, the discriminant must be strictly positive, so (m + 4)^2 - 4(1)(1) > 0. This simplifies to (m + 4)^2 > 4, which means m + 4 > 2 or m + 4 < -2. Solving these inequalities gives m > -2 or m < -6. This corresponds to the intervals (-infinity, -6) or (-2, infinity), matching options A or C.

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