Question

Write the following equation as a quadratic equation in standard form (with = 0). Make sure to remove any brackets and fractions present. (3)/(x) = (5)/(2) = 2x.

A. 2x² -(5)/(2)x - 3 = 0.
B. 2x² −5x−6=0.
C. 3x²− 5x − 10 = 0.
D. 3x² -(5)/(2)x − 3 = 0.

Answer 1

A. 2x² -(5)/(2)x - 3 = 0.

Step-by-step explanation:

(3)/(x) = (5)/(2) = 2x has two = signs. We'll assume the eqaution was meant to be:

(3)/(x) + (5)/(2) = 2x

3 + 5x/2 = 2x^2 [Multiply both sides by x]

2x^2 - (5/2)x - 3 = 0

A. 2x² -(5)/(2)x - 3 = 0.

Answer 2

The correct answer is D. 2x² - (5/2)x - 3 = 0. The equation is multiplied by x to remove the fraction and then rearranged into the standard form of a quadratic equation.

Step-by-step explanation:

To rewrite the equation (3)/(x) = (5)/(2) + 2x as a quadratic equation in standard form, we need to first eliminate the fractions and then rearrange the terms. Multiplying every term by x to get rid of the fraction gives us 3 = (5/2)x + 2x^2. To combine like terms, let's multiply 2x^2 by 2/2 to have common denominators, yielding 3 = (5/2)x + (4/2)x^2. Now, rearranging and combining like terms to form ax² + bx + c = 0, we get 2x² - (5/2)x - 3 = 0, which is option D. Note that option A is incorrect because it suggests multiplying 5/2 by 2 in the term (5/2)x, which is unnecessary and incorrect; option B incorrectly converts the fractions; and option C is incorrect because it misrepresents the coefficients of x and x².