Which expression is equivalent to 2x² - 2x + 7?

Solution:

To check whether the solution exists for a particular quadratic equation ax² + bx + c or not, we check the discriminant D = b² - 4ac.

We know that quadratic equations can have at most two roots by definition.

Let us calculate the discriminant here

D = (-2)² - 4(7)(2) = -52 < 0

As the discriminant is less than zero, the quadratic equation has no real roots.

Hence, the quadratic equation given has two complex roots.

Using the quadratic formula, we get the solutions of the equation.

⇒ x = (2 ± 2√13i) / 4

⇒ x = 0.5 ± √13i / 2

Now, we write the equation in the form of (x - a)(x - b), where a, b are the roots of the equation.

⇒ 2x² – 2x + 7 = (x - 0.5 - √13i / 2)(x - 0.5 + √13i / 2)

Hence, the expression which is equivalent to 2x² – 2x + 7 is (x - 0.5 - √13i / 2)(x - 0.5 + √13i / 2).]

Which expression is equivalent to 2x² - 2x + 7?

Summary:

The expression which is equivalent to 2x² - 2x + 7 is (x - 0.5 - √13i / 2)(x - 0.5 + √13i / 2).