Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, = 1,x, = 2,x3 = 3,x, = 4 , and x5 = 5 can be written as Р(2) %— со + с, (х - 1) + с, (х — 1)(х — 2) + с, (х — 1)(х — 2)(х — 3) +C,(х — 1)(х — 2)(х — 3)(х — 4). What is 2a ?

Q: A quadratic polynomial y = 4x2 +7x -3 has roots p and q. Find a quadratic g(x) = x² + ax +B with…

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Q: Could you explain how to do this in detail

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Q: 22. Find the zeros off (x) = x³ – 4x² + x + 6

A: we have to find roots

Q: If P(x)=x2+x+3 and Q(x)=5x2−1​, find Q (1/4)

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Q: If h(z) = 2x2 - 3r +1, what is h(-2)?

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Q: 1) Factor f(x) = 2x3 + (-3-2i)x? + (-3- i)x + (2 + i) into linear factors 2 +i is a zero of the…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Which polynomial is equal to (x + 1) divided by (x + 1)? А - х3 — х2 -х+1 В — х3 + х2 — х + 1 B x*.…

A: WE HAVE TO FIND ANSWER

Q: If  f(x) = ax2 − 27x − 7  has the roots  −  1 4  and 7, find the value of a.

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Q: Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial…

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Q: Let f(x) = 2x + 8, g(x) h(x) — 3х — 6. = x + 2x – 8,and Perform the indicated operation. (Simplify…

A: Given that fx=2x+8,gx=x2+2x-8 and hx=3x-6To find :f-gxSolution :f-gx=fx-gx=2x+8-x2+2x-8…

Q: Suppose 7x-19 f(x)= x2 6x 9 Then В f(x) х-3 (х-3)? and B = where A

A: Given function is

Q: Select all the expressions that are equivalent to (3z + 2) (1 – 4) for all real values of x. A; 3z²…

A: We have to select the expressions that are equivalent to given function. This problem can be done…

Q: Determine whether the following polynomials are even, odd, or neither. (A) f (x) = 5a – 2a- 4x + 1…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.