A cubic spline S is defined by: (S,(x) = 3(x - 1) + 2(x – 1)² – (x – 1)ª S(x) = s,(x) = 4 + 4(x – 2) – (x– 2)* +(x - 2) ifisxs2 if 25x53 Sis a natural cubic Spline True O False

Q: 2 17. The polynomial P(x) = x* - &x – of x = 1, 3, and -2+i. What is its fourth zero? 8x +15 has…

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Q: 3. If p = 4x3 + x² + 2x + 5 and %3D q = 6x3 + 3x² + x + 2 Find the product in p and q, ||p|| and…

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Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, =1,x2…

A: Firstly make the divided difference table x P(x) Pxi , xj Pxi , xj , xk Pxi , xj , xk , xl Pxi ,…

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

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Q: 3 3 Let AÄx) = (10x – 15) + 9 and g(x) = (16 – 8x) – 7. Find all values of x for which g(x) < f(x).

A: Given: fx=3510x-15+9 gx=3816-8x-7 When, gx≤fx…

Q: If β is a zero of x2 +x + 2 over Z5, find the other zero.

A: Given: The expression x2+x+2 over  Z5 has β as zero. To find: The other zero of the given…

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, = 1,x2…

A: The objective is to find the value of 2c3-c2

Q: 3. (12 points) Given f(x) = −0.25x3(x − 2)² (x + 1)4 - Find all of the zeros and state their…

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Q: The quadratic form X1 e x2 = x} – 2x1X2 + x} + x} %3D - X3 on 3 is Positive definite Positive…

A: The solution is given as

Q: Q.29 Expand the following: (i) (4a– 2b–3c) (ii) | 2p -3 || 2p 1 y+-z (iii)

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Using Newton's Divided Difference, the polynomial that interpolates x + sinx at the points x, =1,x2…

A: Newton's Divided Difference table is given by x P(x) Pxi , xj Pxi , xj , xk Pxi , xj , xk , xl…

Q: Find the 1-/2a2-1 limr 1 x-1 O 1 O -2 None of these

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

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Q: Which polynomial function has the following end behavior? Assume a and k are positive constants. If…

A: Given: If x→-∞ then p(x)→+∞,   If x→+∞ then p(x)→-∞

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

A: topic- quadratic equations for equation ax2+bx+c=0sum of roots=-baproduct of roots=ca

Q: 29. The area of the shaded region shown below can be represented as (2x + 6) (2x + 6) - (r(x + 3)²).…

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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: Which polynomial function in standard form has a root of multiplicity 1 at x= 3, and a root of…

A: A polynomial function has a root of multiplicity 1 at x=3, and a root of multiplicity 2 at x=4

Q: Let g(x) = 4x3 + 4x - 10x2x3 be a quadratic form in three variables. Find a quadratic form of the…

A: Given: g(x)= 4x22+4x32 -10x2 x3 The matrix of the…

Q: 1. Fill in the table below with information about each of the following polynomials. Polynomial…

A: We have to find the degree and the end behaviour of the polynomial.

Q: Given w(x) 5a +6 and z(x) = 3x – 4, evaluate the following. %3D %3D (a) (w o z)( – 1) = %3D (b) (z o…

A: Consider the given information. wx=5x+6zx=3x2−4 Find the composition of the function as,…

Q: 5. (x5 + 25x3 -7x2 +37x 18) + (*+5) %3D II. A. Use the REMAINDER THEOREM to find the remainder of…

A: We have to solve

Q: The envelope below has a mailing label. L(x) = 6x + 5

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Q: What is the fully factored form (with real coefficients) for the polynomial f(x) = æ® – 1? (Hint: 16…

A: Consider the given polynomial

Q: 6) Find a polynomial funclion with the given zeros: 0, -1, 2. (a) S(r) = x(x - 1)(r + 2) (b) f(t) =…

A: f(x) is zero at the given zeros

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.