If the polynomial 2x³ + ax² + 3x - 5 and x³ + x² - 4x + a leave the same remainder when divided by x - 2 , find the value of a
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Answered by
1
Step-by-step explanation:
Let the given polynomials be f(x) and g(x).
When f(x) and g(x) are divided by (x-2) they leave the same remainder.
I.e (x-2) is a factor of f(x) and g(x). It means 2 is the zero of f(x) and g(x)
So that,
f(2) = g(2)
2x³+ax²+3x-5 = x³+x²-4x+a
2(2)³+a(2)²+3(2)-5 = 2³+2²-4(2)+a
2(8)+a(4)+6-5 = 8+4-8+a
16+4a+1 = 4+a
17+4a = 4+a
4a-a = 4-17
3a = -13
a = -13/3.
Answered by
16
Let the given polynomials be f(x) and g(x).
When f(x) and g(x) are divided by (x-2) they leave the same remainder.
(x-2) is a factor of f(x) and g(x).
It means 2 is the zero of f(x) and g(x)
Thankyou :)
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