Final answer:
The equation x⁴-3x²-10=0 can be treated as a quadratic in form, which after finding values for u (the substitution for x²), yields four real distinct solutions, hence option (c) is correct.
Step-by-step explanation:
The given equation is x⁴-3x²-10=0. This can be approached as a quadratic equation in the form of ax²+bx+c=0 by making a substitution, let u=x². The equation then becomes u²-3u-10=0, which is a quadratic equation. Solving for u using the quadratic formula, u=(-b±√(b²-4ac))/(2a), we can then find the corresponding x values by taking the square root of each u value.
If the discriminant (the part under the square root in the quadratic formula, b²-4ac) is positive, we get two real solutions for u, each of which can give us two x values, resulting in four real distinct solutions for the original equation. If it is zero, we get one value for u, but the nature of square roots gives us two x values (one positive and one negative), resulting in two real solutions with the same absolute value but opposite signs. If the discriminant is negative, there would only be complex solutions for u, and hence no real x values would be possible, which is not the case here.
By applying the quadratic formula and interpreting the results, we can determine that option (c) has four real distinct solutions is correct for the equation provided.