Multiple choice

If the equation $ax^{2}$+10x+a= 0 has distinct real roots then the possible value of a is.

  1. -6

  2. -5

  3. -4

  4. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For distinct real roots, discriminant D > 0. D = 10^2 - 4(a)(a) = 100 - 4a^2. 100 - 4a^2 > 0 implies a^2 < 25, so -5 < a < 5. Among options, -4 is the only value in the range.

AI explanation

For the equation ax^2 + 10x + a = 0 to have distinct real roots, the discriminant must be strictly positive. We set the discriminant D = 10^2 - 4(a)(a) > 0, which simplifies to 100 - 4a^2 > 0. Dividing by 4 gives 25 > a^2, meaning the absolute value of a must be strictly less than 5. Checking the given options, the only value satisfying this condition is -4.

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