Question

Find the roots of the quadratic equation a² – 3a – 54 = 0​

Answer 1

Use the quadratic formula

$=−±2−4√2$

$x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}x=2a−b±b2−4ac$

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

$2−3−54=0$

$a^{2}-3a-54=0a2−3a−54=0$

$=1$

$a={\color{#c92786}{1}}a=1$

$=−3$

$b={\color{#e8710a}{-3}}b=−3$

$=−54$

$c={\color{#129eaf}{-54}}c=−54$

$=−(−3)±(−3)2−4⋅1(−54)√2⋅1$

$a=\frac{-({\color{#e8710a}{-3}}) \pm \sqrt{({\color{#e8710a}{-3}})^{2}-4 \cdot {\color{#c92786}{1}}({\color{#129eaf}{-54}})}}{2 \cdot {\color{#c92786}{1}}}a=2⋅1−(−3)±(−3)2−4⋅1(−54)$

Simplify

Evaluate the exponent

Multiply the numbers

Add the numbers

Evaluate the square root

Multiply the numbers

=3±152

$a=\frac{3 \pm 15}{2}a=23±15$

Separate the equations

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

$=3+152$

$a=\frac{3+15}{2}a=23+15$

$=3−152$

$a=\frac{3-15}{2}a=23−15$

Solve

Rearrange and isolate the variable to find each solution

=9

a=9a=9

=−6

Solution

=9=−6