Question

Which statement is true about the equation 10x²−x+9=0?

(a) It has one solution.
(b) It has two real, irrational number solutions.
(c) It has two real, rational number solutions.
(d) It has no real number solutions.

Answer 1

The equation 10x²−x+9=0 has no real number solutions.

Step-by-step explanation:

The equation 10x²−x+9=0 is a quadratic equation, which means it is in the form ax²+bx+c=0, where a, b, and c are constants. To determine the number of solutions this equation has, we can use the discriminant, which is given by b²-4ac.

In this case, a=10, b=-1, and c=9. Plugging these values into the discriminant formula, we get (-1)²-4(10)(9) = 1-360 = -359.

Since the discriminant is negative, the equation has no real number solutions. Therefore, the correct answer is (d) It has no real number solutions.