please help me solve this question
Answers
let the given polynomial be
if f(x) is exactly divisible by (x-1).
if f(x) is exactly divisible by (x-2).
subtracting eq(2) by eq(1):
put a = -37 in eq(1):
thus the value of a is -37 and value of b is 26.
hope this helps you.
cheers!!
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student-name Annie answered this
15 helpful votes in Math, Class IX
ANS: Let p(x) = x3 - 10x2 +ax +b Using factor theorem we find that if p(x) is divided by x-1 the remainder, i.e. p(1) = 0
Therefore, p(1) = (1)3 - 10(1)2 + a(1) +b = 0
=> 1 - 10 +a +b =0
=> a+ b = 9=> b = 9-a .........equation (1)
In the same way if p(x) is divided by x-2 the remainder, i.e. p(2) = 0 Therefore, p(2) = (2)3 - 10(2)2 + a(2) +b = 0
=> 8 - 40 +2a +b =0=> -32+2a+b=0...........equation (2)
Substituting the value of equation(1) in equation(2) we get, -32 + 2a+9 -a = 0
=> a = 23
Substituting the value of a in equation (1) we get b= 9- 23
=> b = -14
Hence, a=23 and b=-14
Was this answer helpful18
student-name Annie answered this
15 helpful votes in Math, Class IX
ANS: Let p(x) = x 3 + 10x 2 +ax +b Using factor theorem we find that if p(x) is divided by x-1 the remainder, i.e. p(1) = 0
Therefore, p(1) = (1)3 + 10(1)2 + a(1) +b = 0
=> 1 + 10 +a +b =0
=> a+ b = 11=> b = -11-a .........equation (1)
In the same way if p(x) is divided by x-2 the remainder, i.e. p(2) = 0 Therefore, p(2) = (2)3 + 10(2)2 + a(2) +b = 0
=> 8 + 40 +2a +b =0=> 48+2a+b=0...........equation (2)
Substituting the value of equation(1) in equation(2) we get, 48 + 2a - 11 - a = 0
=> a = -37
Substituting the value of a in equation (1) we get b= 9- (-59)
=> b = 46
Hence, a=-37 and b=46
Was this answer helpful3
student-name Annie answered this
15 helpful votes in Math, Class IX
ANS: Let p(x) = x 3 + 10x 2 +ax +b Using factor theorem we find that if p(x) is divided by x-1 the remainder, i.e. p(1) = 0
Therefore, p(1) = (1)3 + 10(1)2 + a(1) +b = 0
=> 1 + 10 +a +b =0
=> a+ b = 11=> b = 11-a .........equation (1)
In the same way if p(x) is divided by x-2 the remainder, i.e. p(2) = 0 Therefore, p(2) = (2)3 + 10(2)2 + a(2) +b = 0
=> 8 + 40 +2a +b =0=> 48+2a+b=0...........equation (2)
Substituting the value of equation(1) in equation(2) we get, 48 + 2a + 11 - a = 0
=> a = -59
Substituting the value of a in equation (1) we get b= 9- (-59)
=> b = 68
Hence, a=-59 and b=68
so this is the answer
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