Question

Use the discriminate to determine how many solutions this equation has -8x^2-8x-2=0

Answer 1

• -8x²-8x-2=0

Here

• a=-8
• b=-8
• c=-2

Discriminate

• D=b²-4ac
• D=(-8)²-4(-8)(-2)
• D=64-64
• D=0

Roots are equal hence one solution

Answer 2

One solution

Explanation:

Discriminant

`\textsf{Discriminant}:b^2-4ac}\quad\textsf{when}\:ax^2+bx+c=0`

`\textsf{If}\quad b^2-4ac=0 \implies \textsf{one solution}`

`\textsf{If}\quad b^2-4ac > 0 \implies \textsf{two solutions}`

`\textsf{If}\quad b^2-4ac < 0 \implies \textsf{no solutions}`

Given equation:

`-8x^2-8x-2=0`

Swap sides:

`\implies 8x^2+8x+2=0`

Using discriminant:

`\implies b^2-4ac=8^2-4(8)(2)=0`

Therefore, there is one solution

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Proof

`8x^2+8x+2=0`

Divide both sides by 2:

`\implies 4x^2+4x+1=0`

Separate the middle term:

`\implies 4x^2+2x+2x+1=0`

Factor the first two terms and the last two terms separately:

`\implies 2x(2x+1)+1(2x+1)=0`

Factor out the common term
`(2x+1)`:

`\implies (2x+1)(2x+1)=0`

Therefore:

`\implies 2x+1=0`

`\implies x=-\frac12`

Thus proving there is one solution.