Question

find the root of x²-6x+4=0 using quadratic formula​

Answer 1

Step-by-step explanation:

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Answer 2

Given: The equation is$x^2-6x+4=0$

We have to find the root of the above equation.

We are solving in the following way:

Using the Quadratic Formula where$a = 1, b = -6, \ and\ c = 4$

The formula for the quadratic equation is:

$\begin{array}{c}x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} \\\end{array}$

By putting the values in the formula:

$\begin{array}{c}\\=>x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} \\\\=>x=\frac{-(-6) \pm \sqrt{(-6)^{2}-4(1)(4)}}{2(1)} \\\\=>x=\frac{6 \pm \sqrt{36-16}}{2} \\\\=>x=\frac{6 \pm \sqrt{20}}{2}\end{array}$

The discriminant$b^2-4ac>0$

so, there are two real roots.

Now simplifying the above equation:

$\begin{array}{l}=>x=\frac{6 \pm 2 \sqrt{5}}{2} \\\\=>x=\frac{6}{2} \pm \frac{2 \sqrt{5}}{2}\end{array}$

Simplifying fractions and/or signs:

$x=3 \pm \sqrt{5}$

Which becomes,

$=>x=5.23607\\=> x=0.763932$

Hence, the roots of the above equation are$x=5.23607 \ and\ x=0.763932$