Which expression is equivalent to 2x2 – 2x + 7?
To check whether the solution exists for a particular quadratic equation ax2 + bx + c or not, we check the discriminant D = b2 - 4ac.
Answer: The expression which is equivalent to 2x2 – 2x + 7 is (x - 0.5 - √13i / 2)(x - 0.5 + √13i / 2).
Let's understand the solution in detail.
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)