Question

if px^2 + 3x + q =0 has two roots x= -1 & x= -2 , the value of q - p is
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Answer 1

p(-1)² + 3(-1) + q = 0

p -3 + q = 0

p + q = 3

-(-p) -(-q) = 3

-( p - q ) = 3

p - q = -3

Answer 2

REQUIRED SOLUTION:-

GIVEN,

p(x) = px² + 3x + q =0

where, -1 and -2 are its zeros.

TO FIND,

the value of q-p.

SOLUTION,

p(x) = px² + 3x + q

Putting, x = -2 in p(x)

px²  + 3x  + q  = 0

p(-2)² + 3(-2) +q = 0

p(4) -6 +q = 0

4p +q = 6……………..(1)

Putting x= -1 in p(x),

px²  + 3x  + q  = 0

p(-1)² + 3(-1) +q = 0

p(1) -3 +q = 0

p +q = 3……………..(2)

On subtracting equation (1) and (2)

4p +q = 6

p +q = 3

(-)  (-)  (-)

3p = 3

p= 3/3

p = 1

On substituting p= 1 in equation 1,

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

Hope it helps :)