The discriminant of a quadratic equation is 35. The roots are:

a) unequal rational numbers
b) unequal irrational numbers
c) equal rational numbers
d) imaginary numbers

Please explain.

It is B.

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To determine the nature of the roots of a quadratic equation based on its discriminant, we can use the following criteria:

1) If the discriminant (denoted as Δ) is greater than 0 (Δ > 0), the equation will have two distinct real roots.
2) If the discriminant is equal to 0 (Δ = 0), the equation will have two identical real roots.
3) If the discriminant is less than 0 (Δ < 0), the equation will have two complex conjugate roots (which are imaginary).

In the given question, the discriminant of the quadratic equation is 35. Since 35 is a positive value (Δ > 0), we can conclude that the quadratic equation will have two distinct real roots.

Therefore, the correct option is:

a) unequal rational numbers

To determine the roots of a quadratic equation, we need to consider its discriminant. The discriminant is calculated using the formula: b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.

In this case, you mentioned that the discriminant value is 35. Therefore, the equation becomes b^2 - 4ac = 35.

Based on the discriminant value, we can determine the nature of the roots as follows:

1. If the discriminant is a perfect square (e.g., 0, 1, 4, 9, 16, etc.), then the roots are "equal rational numbers". This means that the roots of the equation are the same and can be expressed as a fraction of two integers.

2. If the discriminant is a positive but non-perfect square, such as 35 in this case, the roots are "unequal irrational numbers". This means that the roots are different and cannot be expressed as fractions or integers, but as non-repeating decimals.

3. If the discriminant is negative, such as -35, then the roots of the equation are "imaginary numbers". Imaginary numbers are expressed in terms of the imaginary unit i, where i^2 = -1.

Therefore, in this case, since the discriminant is 35, the roots of the quadratic equation are "unequal irrational numbers" (option b).

I think it's B, unequal irrational numbers. But if the discriminant is 35 then this is not a perfect square.

Do they give you the whole equation such as x^2 + 6x + 5 = 0?