For the equation y = 3x² − 4x + 11, choose the correct application of the quadratic formula.

An algebraic expression in the form of ax² + bx + c = 0 is called a quadratic equation, a ≠ 0.

Answer: The value of x for the equation y = 3x² − 4x + 11 using quadratic formula is 2/3 + i √29 / 3 or  2/3 - i √29 / 3

Let's find the solution using the quadratic formula.

Explanation:

Quadratic formula is  x = − b ± √ b² − 4 a c / 2a 

Where a is the coeffient of x² , b is coefficient of x and c is the constant term.

⇒x = − b ± √ b² − 4 a c / 2a

⇒ x = − (- 4) ± √ (- 4)² − 4 × 3 × 11 / 2 (3)

⇒ x =  − (- 4) ± √ 16 − 132 / 6

⇒ x =  − (- 4) ± √ 16 − 132 / 6

⇒ x =  − (- 4) ± √ -116 / 6

⇒ x =  − (- 4) ± i2√ 29 / 6

We will have two values of x 

⇒ x = 2/3 + i √29 / 3 or  2/3 - i √29 / 3

Try out Cuemath's Quadratic Equation Calculator to find the solutions to a quadratic equation.

Thus, the value of x for the equation y = 3x² − 4x + 11 using quadratic formula is 2/3 + i √29 / 3 or  2/3 - i √29 / 3