Find the solutions of the following equations: a) (i) x^(2)-3x+1=0

Identify coefficients: Step 1: Identify coefficients a, b, and c from the equation x^2 - 3x + 1 = 0. a = 1, b = -3, c = 1 Use quadratic formula: Step 2: Use the quadratic formula x = (-b ± sqrt(b^2 - 4ac)) / (2a). Substitute a = 1, b = -3, c = 1 into the formula. x = (-(-3) ± sqrt((-3)^2 - 4*1*1)) / (2*1) Simplify expression: Step 3: Simplify the expression under the square root. sqrt(9 - 4) = sqrt(5) Continue with formula: Step 4: Continue with the quadratic formula. x = (3 ± sqrt(5)) / 2 Write roots in simplest form: Step 5: Write the roots in simplest form. Roots are x = (3 + sqrt(5)) / 2 and x = (3 - sqrt(5)) / 2

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Algebra 1

Factor quadratics with leading coefficient 1

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Q. Find the solutions of the following equation:

\newline

x^{2}-3 x+1=0

Identify coefficients: Identify coefficients $a$ , $b$ , and $c$ from the equation $x^2 - 3x + 1 = 0$ . $\newline$ $a = 1$ , $b = -3$ and $c = 1$ .
Use quadratic formula: Use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ . $\newline$ Substitute $a = 1$ , $b = -3$ , $c = 1$ into the formula. $\newline$ $x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot 1\cdot 1}}{2\cdot 1}$
Simplify expression: Simplify the expression under the square root. $\newline$ $\sqrt{9 - 4} = \sqrt{5}$
Continue with formula: Continue with the quadratic formula. $\newline$ $x = \frac{3 \pm \sqrt{5}}{2}$
Write roots in simplest form: Write the roots in simplest form. $\newline$ Roots are $x = \frac{3 + \sqrt{5}}{2}$ and $x = \frac{3 - \sqrt{5}}{2}$