For the quadratic equation x^2 + 4x + 3 = 0, the discriminant is?

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Multiple Choice

For the quadratic equation x^2 + 4x + 3 = 0, the discriminant is?

Explanation:
For a quadratic, the discriminant tells how many real solutions the equation has. It’s computed as D = b^2 - 4ac. Here a = 1, b = 4, c = 3, so D = 4^2 - 4(1)(3) = 16 - 12 = 4. Since the discriminant is positive, there are two distinct real roots (and in fact the equation factors to (x + 1)(x + 3) giving x = -1 and x = -3). So the discriminant value is 4, which matches the correct choice. The other numbers would imply different situations: 0 would mean a repeated root; a negative value would mean complex roots; 12 is 4ac, not the discriminant.

For a quadratic, the discriminant tells how many real solutions the equation has. It’s computed as D = b^2 - 4ac.

Here a = 1, b = 4, c = 3, so D = 4^2 - 4(1)(3) = 16 - 12 = 4. Since the discriminant is positive, there are two distinct real roots (and in fact the equation factors to (x + 1)(x + 3) giving x = -1 and x = -3).

So the discriminant value is 4, which matches the correct choice. The other numbers would imply different situations: 0 would mean a repeated root; a negative value would mean complex roots; 12 is 4ac, not the discriminant.

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