Respuesta :
Question :-
- If one root of the equation [tex]\sf x^2 +px +8 =0 [/tex] is -2 then find the value of P.
[tex] \bigstar \large \purple{ \pmb {\underline{ \sf Explanation:-}}}[/tex]
- 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.
[tex]\qquad[/tex][tex]\pink{ \bf \longrightarrow x^2 +px +8 = 0}[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow (-2)^2 + p \times -2 +8 = 0[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 4 - 2p +8 = 0[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow 12 -2p = 0[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow -2p = -12[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow \cancel{-}2p = \cancel{-}12[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow p = \dfrac{12}{2}[/tex]
[tex]\qquad[/tex][tex] \sf \longrightarrow p =\cancel{ \dfrac{12}{2}}[/tex]
[tex]\qquad[/tex][tex]\pink{ \bf \longrightarrow p = 6}[/tex]
- Henceforth, p will be 6.
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.
[tex] \: [/tex]
Solution :
[tex] \\ \sf \: \dashrightarrow \: x²+ px + 8 = 0[/tex]
Now putting the value of x in the equation :
[tex] \sf \dashrightarrow \: {( - 2)}^{2} + p( - 2) + 8 = 0[/tex]
[tex] \sf \dashrightarrow \: 4 + ( - 2p) + 8 = 0[/tex]
Adding the like terms :
[tex]\sf \dashrightarrow \: - 2p + 12 = 0[/tex]
Transposing 12 to the right side thus it becomes negative :
[tex]\sf \dashrightarrow \: - 2p = - 12[/tex]
Cancelling (-) from both sides :
[tex]\sf \dashrightarrow \: \cancel{-} 2p = \cancel{-} 12[/tex]
[tex]\sf \dashrightarrow \: p = \dfrac{12}{2} [/tex]
[tex] \dashrightarrow \sf \: p = 6[/tex]
