If f(x)=x^4 -2 x^3 -3 x^2 -ax+ b is divided by x-1 and x--1 the remainders are 5 and 19 respectively find the value of a and b
1 answer:
On dividing, f(x) by (x-1) we get remainder =b-a-4
And ,we are given the remainder is 5
So, b-a-4=5
And, On dividing f(x) by (x+1) we get remainder=b+a
So, b+a=19
As, b-a-4=5 And b+a=19
To solve for a and b let us add the two equations
So, 2b+0a-4=5+19
Or. 2b-4=24
Adding 4 on both sides we get
2b-4+4=24+4
2b=28
Divide by 2 on both sides
2b/2=28/2
b=14
As, a+b=19 and b=14
So, a+14=19
Subtracting 14 from both sides, we get
a+14-14=19-14
a+0=5
a=5
So, a=5 and b=14
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<h3>What is meant by definite integral?</h3>
A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.
Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.
If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.
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To learn more about definite integral refer to:
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