if x cube + p multiplied by x square + qx + 6 leaves remainder 3 when divided by x-3 and leaves 0 when divided by x-2 , find the value of p and q. lesson- polynomial
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Answered by
102
Hey there!
f(x) = x³+px²+qx+6
f(3) = 3³+p(3²)+q(3)+6=3
=>27+p(9)+3q+6=3
=>33+9p+3q=3
=>3(3p+q)=3-33
=>3(3p+q)=-30
=>3p+q=-10 ---(1)
-----------------------------------------------------------------------------------
f(2) = 2³+p(2²)+q(2)+6=0
=>8+4p+2q+6=0
=>14+4p+2q
=>2(2p+q)=-14
=>2p+q=-7 ___(2)
(1)-(2)
3p+q=-10
2p+q =-7
------------
p = -3
2p+q = -7
-6+q =-7
q= -1
(p,q) = (-3,-1)
★ hope helped! a ★
f(x) = x³+px²+qx+6
f(3) = 3³+p(3²)+q(3)+6=3
=>27+p(9)+3q+6=3
=>33+9p+3q=3
=>3(3p+q)=3-33
=>3(3p+q)=-30
=>3p+q=-10 ---(1)
-----------------------------------------------------------------------------------
f(2) = 2³+p(2²)+q(2)+6=0
=>8+4p+2q+6=0
=>14+4p+2q
=>2(2p+q)=-14
=>2p+q=-7 ___(2)
(1)-(2)
3p+q=-10
2p+q =-7
------------
p = -3
2p+q = -7
-6+q =-7
q= -1
(p,q) = (-3,-1)
★ hope helped! a ★
vaishnavi91:
so inteligent
Answered by
12
Answer:
p=-3. q=-1
Step-by-step explanation:
Answer is always right
I think so
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