Question

Thw sum of roots of the equation 3x²-7x+1=0​

Answer 1

1) Use the quadratic formula

$x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}</p><p>$

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

$3x^{2}-7x+1=0$

$a={\color{#c92786}{3}}$

$b={\color{#e8710a}{-7}}$

$</p><p>c={\color{#129eaf}{1}}$

$x=\frac{-({\color{#e8710a}{-7}}) \pm \sqrt{({\color{#e8710a}{-7}})^{2}-4 \cdot {\color{#c92786}{3}} \cdot {\color{#129eaf}{1}}}}{2 \cdot {\color{#c92786}{3}}}</p><p>$

2)Simplify

• Evaluate the exponent
• Multiply the numbers
• Subtract the numbers
• Multiply the numbers

$x=\frac{7 \pm \sqrt{37}}{6}$

3)Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

$x=\frac{7+\sqrt{37}}{6}</p><p>$

$x=\frac{7-\sqrt{37}}{6}$

4) solve

Rearrange and isolate the variable to find each solution

$x=\frac{7+\sqrt{37}}{6}$

$x=\frac{7-\sqrt{37}}{6}$

Solution

$x=\frac{7 \pm \sqrt{37}}{6}$