Question

Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. 8(x2 + 2x + 1) = –3 + 8 x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot x = –1 Plus or minus StartRoot StartFraction 4 Over 8 EndFraction EndRoot 8(x2 + 2x + 1) = 3 + 1 8(x2 + 2x) = –3

Answer 1

Polynomial expressions of
`2^(nd)` degree with one unknown (only
`x`) have
`2` roots. We use the formula below to determine these roots;

• 
  `x_(1)=(-b+√(b^2-4(ac)) )/(2a)`
• 
  `x_(2)=(-b-√(b^2-4(ac)) )/(2a)`

This formula is valid for equations of the form
`ax^2+bx+c`. We can convert the equation given in the question into this format to get the result;

• 
  `ax^2+bx+c = 8x^2+16x+3=0`

Hence, the value of
`a`:
`8`,

the value of
`b`:
`16`,

the value of
`c`:
`3`.

Now, we can find the roots of this equation by using this formula;

• 
  `x_(1)=(-16+√(160) )/(16) = (-4+√(10))/(4)`
• 
  `x_(2)=(-16-√(160) )/(16)=(-4-√(10))/(4)`