Explanation Given: The trinomial is y 2 + b y + 20 . Calculation: We begin by writing the first terms of the binomial factors. ( y + p ) ( y + q ) Here, sum of numbers = coefficient of x p + q = b Product of numbers = constant p · q = 20 Now, we will assume combinations of factors for sum of numbers and product of numbers. Here, we take only positive factors because when weadd them, we get a positive number [ b is a positive value] and when we multiply them, we get a positive number

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

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Chapter 13.2, Problem 96ES

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The positive value of b so that y2+by+20 is factorable.

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Chapter 13.2, Problem 95ES

Chapter 13.2, Problem 97ES

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R denotes the field of real numbers, Q denotes the field of rationals, and Fp denotes the field of p elements given by integers modulo p. You may refer to general results from lectures. Question 1 For each non-negative integer m, let R[x]m denote the vector space consisting of the polynomials in x with coefficients in R and of degree ≤ m. x²+2, V3 = 5. Prove that (V1, V2, V3) is a linearly independent (a) Let vi = x, V2 = list in R[x] 3. (b) Let V1, V2, V3 be as defined in (a). Find a vector v € R[×]3 such that (V1, V2, V3, V4) is a basis of R[x] 3. [8] [6] (c) Prove that the map ƒ from R[x] 2 to R[x]3 given by f(p(x)) = xp(x) — xp(0) is a linear map. [6] (d) Write down the matrix for the map ƒ defined in (c) with respect to the basis (2,2x + 1, x²) of R[x] 2 and the basis (1, x, x², x³) of R[x] 3. [5]

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part b please

Chapter 13 Solutions

EBK ALGEBRA FOUNDATIONS

Ch. 13.1 - Prob. 1VRVC Ch. 13.1 - Prob. 2VRVC Ch. 13.1 - Prob. 3VRVC Ch. 13.1 - Prob. 4VRVC Ch. 13.1 - Prob. 5VRVC Ch. 13.1 - Prob. 6VRVC Ch. 13.1 - Prob. 1ES Ch. 13.1 - Prob. 2ES Ch. 13.1 - Prob. 3ES Ch. 13.1 - Prob. 4ES

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The positive value of b so that y 2 + b y + 20 is factorable.

Solution Summary: The author explains that the positive value of b is factorable. The trinomial is y2+by+20.

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The positive value of b so that y2+by+20 is factorable.

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