Use the Quadratic Formula to solve the quadratic below x^(2)-5x+9=0 Desmos Scientific Calculator Show Your Work

Question

Use the Quadratic Formula to solve the quadratic below  x^(2)-5x+9=0 Desmos Scientific Calculator Show Your Work

Bytelearn · Accepted Answer

Identify coefficients: Identify the coefficients a, b, and c in the quadratic equation x^2 - 5x + 9 = 0. The standard form of a quadratic equation is ax^2 + bx + c = 0. Comparing this with our equation, we find that a = 1, b = -5, and c = 9.Write Quadratic Formula: Write down the Quadratic Formula. The Quadratic Formula is (-b ± √(b^2 - 4ac)) / (2a). We will use this formula to find the roots of the equation.Substitute values: Substitute the values of a, b, and c into the Quadratic Formula. Substitute a = 1, b = -5, and c = 9 into the formula to get the roots of the equation. (-(-5) ± √((-5)^2 - 4*1*9)) / (2*1)Simplify terms: Simplify the terms inside the square root and outside. Calculate the discriminant (the expression inside the square root) and simplify the constants outside the square root. (5 ± √(25 - 36)) / 2Simplify square root: Simplify the expression under the square root. Since 25 - 36 is -11, we have a negative number under the square root, which indicates that the roots will be complex numbers. (5 ± √(-11)) / 2Express in terms of i: Express the square root of the negative number in terms of i, where i is the imaginary unit. √(-11) can be written as √(11) * i, since i is defined as √(-1). (5 ± √(11) * i) / 2Divide by 2: Simplify the expression by dividing both terms by 2. Divide the real part and the imaginary part by 2 to get the roots in a+bi form. (5/2) ± (√(11)/2) * iWrite roots in a+bi form: Write the roots in the simplest a+bi form. Express the roots as two separate terms, one with the plus sign and one with the minus sign. 5/2 + (√(11)/2) * i & 5/2 - (√(11)/2) * i

Use the Quadratic Formula to solve the quadratic below $\newline$ $x^{2}-5 x+9=0$ $\newline$ Desmos Scientific Calculator $\newline$ Show Your Work

Full solution

More problems from Quadratic equation with complex roots

Related topics

Use the Quadratic Formula to solve the quadratic below\newlinex2−5x+9=0 x^{2}-5 x+9=0 x2−5x+9=0\newlineDesmos Scientific Calculator\newlineShow Your Work

Use the Quadratic Formula to solve the quadratic below $\newline$ $x^{2}-5 x+9=0$ $\newline$ Desmos Scientific Calculator $\newline$ Show Your Work