if px^2 + 3x + q =0 has two roots x= -1 & x= -2 , the value of q - p is
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1
p(-1)² + 3(-1) + q = 0
p -3 + q = 0
p + q = 3
-(-p) -(-q) = 3
-( p - q ) = 3
p - q = -3
Answered by
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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 :)
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