Question

"Find the type and number of solutions for each equation?

14) 4x2 + 1 = 4x 15) x2 + 2x = 10 16) 2x – x2 = 10 In quadratic form?"

Answer 1

To find the type and number of solutions for the given quadratic equations, rewrite them in the standard form and use the quadratic formula's discriminant. The nature of the solutions depends on whether the discriminant is positive, zero, or negative.

Step-by-step explanation:

To determine the type and number of solutions for each quadratic equation, we can use the quadratic formula, which is applicable for equations in the form ax² + bx + c = 0. For each given equation, we first need to rearrange it into this standard form before applying the quadratic formula.

1. For the equation 4x² + 1 = 4x, we rearrange it to 4x² - 4x + 1 = 0 before applying the quadratic formula.

2. Similarly, the equation x² + 2x = 10 needs to be rearranged to x² + 2x - 10 = 0.

3. The third equation, 2x – x² = 10, is rewritten as –x² + 2x - 10 = 0.

After rewriting in the standard form, we can compute the discriminant b² - 4ac to determine the nature of the solutions for each equation. If the discriminant is positive, there are two distinct real solutions; if it is zero, there is one real solution; and if it is negative, there are two complex solutions.