Answer:
Step-by-step explanation:Finding the Discriminant
In order to solve the equation 10x^2 + 4 = -5, we first need to isolate the variable x. To do this, we will follow these steps:
Subtract 4 from both sides of the equation to isolate the term with the variable x^2. 10x^2 = -5 - 4
Simplify the equation to get: 10x^2 = -9
Now, we need to isolate x. To do this, divide both sides of the equation by 10. x^2 = -9 / 10
Solve for x by taking the square root of both sides of the equation. x = sqrt(-9 / 10)
Simplify the expression to get the value of x. x = sqrt(-0.9)
Since the square root of a negative number is not a real number, the equation 10x^2 + 4 = -5 has no real number solutions.
Discriminant
The discriminant of a quadratic equation is a number that helps us determine the nature of the roots of the equation. It is given by the formula:
Discriminant = b^2 - 4ac
In our equation, a = 10, b = 0, and c = -1.
Plugging these values into the formula, we get:
Discriminant = 0^2 - 4(10)(-1) Discriminant = 0 - 40 Discriminant = -40
Since the discriminant is negative, the equation has no real number solutions.