Question

solve the following quadratic equations and find the solution x²-2x-8=0​

Answer 1

Answer:

Step-by-step explanation:

x2-2x=8 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 − 2 − 8 = 0

x^{2}-2x-8=0

x2−2x−8=0

= 1

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

a=1

= −2

b={\color{#e8710a}{-2}}

b=−2

= − 8

c={\color{#129eaf}{-8}}

c=−8

= − (− 2 ) ± ( − 2) 2 − 4 ⋅ 1 ( − 8 ) √ 2 ⋅ 1

x=\frac{-({\color{#e8710a}{-2}}) \pm \sqrt{({\color{#e8710a}{-2}})^{2}-4 \cdot {\color{#c92786}{1}}({\color{#129eaf}{-8}})}}{2 \cdot {\color{#c92786}{1}}}

x=2⋅1−(−2)±(−2)2−4⋅1(−8)​​

2

Simplify

3

Separate the equations

4

Solve

Solution

= 4 = − 2

Answer 2

Answer:

By splitting the middle term

$x²-2x-8=0$

${x}^{2} - 4x + 2x - 8 = 0$

$x(x - 4) + 2(x - 4) = 0$

$(x + 2)(x - 4) = 0$

Finding roots :-

First root

$x + 2 = 0$

$x = - 2$

Second root

$x - 4 = 0$

$x = 4$

$\bf \small \therefore \: two \: roots \:are \: - 2 \: and \: 4$