Question

If px² + 3x + q = 0 has two roots x = -1, x = -2 and find q - p.

Answer 1

Given: px²  + 3x  + q  = 0…………(1)

Here p and q are unknown constants. Since x= -1 & x= -2 are the solutions of given equation so it will satisfy the given equation.

On putting x= -2 in equation 1,
px²  + 3x  + q  = 0
p(-2)² + 3(-2) +q = 0
p(4) -6 +q = 0
4p +q = 6……………..(2)

On putting x= -1 in equation 1,
px²  + 3x  + q  = 0
p(-1)² + 3(-1) +q = 0
p(1) -3 +q = 0
p +q = 3……………..(3)

On subtracting equation 3  from 2

4p +q = 6
p +q = 3
(-)  (-)  (-)
---------------
3p = 3
p= 3/3
p = 1

On substituting p= 1 in equation 2,
4p +q = 6
4(1) + q = 6
4 +q = 6
q= 6-4

q= 2

We have to find : q - p
q - p = 2 -1= 1

Hence, the value of q -p = 1.

HOPE THIS WILL HELP YOU...

Answer 2

I think it is the ri8 ans,
         First put the value of x=-1,on solving u get
            p-3+q=0 -----<1>
        Next put he value of x=-2,on solving u get
            4p-6+q=0----<2>
solve(subtract) the eqs <2> & <1>, u get :
3p-3=0
p=1------<3>
Now put the value of p in eq 1
 u get 1-2+q=0
          -1+q=0
===> q=1
therefore p-q=1-1=0
hope u got it