Question

If one root of the equation x^2+px+8=0 is -2, then p=

Answer 1

Given :

• If one root of the equation x²+ px + 8 = 0 is -2, then find the value of p.

Understanding the question :

• Here, In this question, it is given the root of the equation which means we have the value of x.
• Now we are to put the value of x which is (-2) and by evaluating it we could find the value of p.

`\:`

Solution :

`\\ \sf \: \dashrightarrow \: x²+ px + 8 = 0`

Now putting the value of x in the equation :

`\sf \dashrightarrow \: {( - 2)}^(2) + p( - 2) + 8 = 0`

`\sf \dashrightarrow \: 4 + ( - 2p) + 8 = 0`

Adding the like terms :

`\sf \dashrightarrow \: - 2p + 12 = 0`

Transposing 12 to the right side thus it becomes negative :

`\sf \dashrightarrow \: - 2p = - 12`

Cancelling (-) from both sides :

`\sf \dashrightarrow \: \cancel{-} 2p = \cancel{-} 12`

`\sf \dashrightarrow \: p = (12)/(2)`

`\dashrightarrow \sf \: p = 6`

Answer 2

Question :-

• If one root of the equation
  `\sf x^2 +px +8 =0` is -2 then find the value of P.

`\bigstar \large \purple{ \pmb {\underline{ \sf Explanation:-}}}`

• In this
• question, we are given the root of the equation which means we have the value of x.By putting given root in equation and equating it with -2 we can find the value of p.

`\qquad`
`\pink{ \bf \longrightarrow x^2 +px +8 = 0}`

`\qquad`
`\sf \longrightarrow (-2)^2 + p * -2 +8 = 0`

`\qquad`
`\sf \longrightarrow 4 - 2p +8 = 0`

`\qquad`
`\sf \longrightarrow 12 -2p = 0`

`\qquad`
`\sf \longrightarrow -2p = -12`

`\qquad`
`\sf \longrightarrow \cancel{-}2p = \cancel{-}12`

`\qquad`
`\sf \longrightarrow p = (12)/(2)`

`\qquad`
`\sf \longrightarrow p =\cancel{ (12)/(2)}`

`\qquad`
`\pink{ \bf \longrightarrow p = 6}`

• Henceforth, p will be 6.