Use the quadratic formula to solve the quadratic equation 222
2x^2 - 9r + 11 = 0.
Express its solutions in the form a ‡ bi
To solve the quadratic equation 2x^2 - 9x + 11 = 0 using the quadratic formula, we first identify the coefficients: a = 2, b = -9, and c = 11.
The quadratic formula states that the solutions to the quadratic equation ax^2 + bx + c = 0 are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Plugging in the coefficients, we have:
x = (-(-9) ± √((-9)^2 - 4(2)(11))) / (2(2))
Simplifying further:
x = (9 ± √(81 - 88)) / 4
= (9 ± √(-7)) / 4
Since we have a negative under the square root, the solutions will be complex numbers. Let's express the results in the form a + bi:
x = (9 ± √7i) / 4
Therefore, the solutions to the quadratic equation 2x^2 - 9x + 11 = 0 are:
x = (9 + √7i) / 4
x = (9 - √7i) / 4
To solve the quadratic equation 2x^2 - 9x + 11 = 0 using the quadratic formula, we first need to identify the coefficients a, b, and c in the general quadratic equation format: ax^2 + bx + c = 0.
In this case, a = 2, b = -9, and c = 11.
The quadratic formula states that the solutions for x can be found using the formula x = (-b ± √(b^2 - 4ac)) / (2a).
Substituting the values into the formula, we get:
x = (-(-9) ± √((-9)^2 - 4 * 2 * 11)) / (2 * 2)
= (9 ± √(81 - 88)) / 4
= (9 ± √(-7)) / 4
Since the discriminant (√(b^2 - 4ac)) results in the square root of a negative number, we can say that the quadratic equation has complex solutions.
Expressing the solutions in the form a + bi, where a and b are real numbers, we can rewrite the solutions as:
x = (9 ± √7i) / 4
Therefore, the solutions to the quadratic equation 2x^2 - 9x + 11 = 0 are (9 + √7i) / 4 and (9 - √7i) / 4.
To solve the quadratic equation 2x^2 - 9x + 11 = 0 using the quadratic formula, you can follow these steps:
Step 1: Identify the values of a, b, and c from the given equation.
In this case, a = 2, b = -9, and c = 11.
Step 2: Plug the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Step 3: Substitute the identified values into the quadratic formula:
x = (-(-9) ± √((-9)^2 - 4(2)(11))) / (2(2))
x = (9 ± √(81 - 88)) / 4
x = (9 ± √(-7)) / 4
Since we have a square root of a negative number (√-7), we can express the solutions in the form a + bi.
Therefore, the solutions to the quadratic equation 2x^2 - 9x + 11 = 0 in the form a + bi are:
x = (9 ± √(-7)) / 4