If x=0 and x=-1 are the roots of the polynomial f(x)= 2x3-3x2+ax+b, find the value of a and b.
Answers
Answered by
191
Hi ,
f( x ) = 2x³ - 3x²+ax + b
i ) if x = 0 is the root of f ( x ) then
f( 0 ) = 0
2 ( 0 )³ - 3 ( 0 ) ² + a × 0 + b = 0
b = 0 ----( 1 )
ii ) if x = - 1 then
f ( - 1 ) = 0
2 ( - 1 )³ - 3 ( - 1 )² + a ( -1 ) + b = 0
-2 -3 - a + 0 = 0 since b= 0
-5 - a = 0
-a = 5
a = -5
Therefore ,
a = -5 , b = 0
I hope this helps you.
:)
f( x ) = 2x³ - 3x²+ax + b
i ) if x = 0 is the root of f ( x ) then
f( 0 ) = 0
2 ( 0 )³ - 3 ( 0 ) ² + a × 0 + b = 0
b = 0 ----( 1 )
ii ) if x = - 1 then
f ( - 1 ) = 0
2 ( - 1 )³ - 3 ( - 1 )² + a ( -1 ) + b = 0
-2 -3 - a + 0 = 0 since b= 0
-5 - a = 0
-a = 5
a = -5
Therefore ,
a = -5 , b = 0
I hope this helps you.
:)
Answered by
49
Heya
Using the remainder theorem
f(0)=0 and f(-1)=0 as 0 and -1 are it's zeroes
2(0)³-3(0)²+a(0)+b=0
b=0
When x=-1
2(-1)³-3(-1)²+a(-1)+0=0
-2-3-a+0=0
-5-a = 0
-a = -5
a=5 and b=0
Using the remainder theorem
f(0)=0 and f(-1)=0 as 0 and -1 are it's zeroes
2(0)³-3(0)²+a(0)+b=0
b=0
When x=-1
2(-1)³-3(-1)²+a(-1)+0=0
-2-3-a+0=0
-5-a = 0
-a = -5
a=5 and b=0
mysticd:
plz , check again.
I've done the changes!
Thnx ^_^
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