Question

If x²+2x+1=0,x²+3x+p=0 have a common root then p is...
Plz anawer the question ​

Answer 1

Answer:

x²+2x+1=0

x²+x+x+1=0

x(x+1)+1(x+1)=0

(x+1)(x+1)=0

→x=-1

Then p=-1

Answer 2

Concept

The roots of the quadratic equation are just the solutions of this equation. They are the values ​​of the variables that satisfy the given equations. A common root is a root that is common to both  given equations. We derived a condition where one root is common and both roots are common.

Given

We have been given two quadratic equation x²+2x+1=0  ...(1) and x²+3x+p=0  ...(2)  and they have a common root

Find

We are asked to determine the value of p.

Solution

It is given that given equation have common roots which means that solution of one equation must satisfy the other equation.

We will find solution of equation (1) by splitting of middle terms method.

$x^2+2x+1=0$

$x^2+(1+1)x+1=0\\x^2+x+x+1=0\\x(x+1)+1(x+1)=0\\(x+1)(x+1)=0\\x=-1 ,-1$

Putting this value in equation (2) ,we get

$(-1)^2+3(-1)+p=0\\1-3+p=0\\p-2=0\\p=2$

Therefore, the value of p is 2 .

#SPJ2