2. Find the equation of the polynomial with roots (-v3, 0) and (7i, 0), real coe

Question

2. Find the equation of the polynomial with roots (-v3, 0) and (7i, 0), real coefficients, and passing through the point (1, 200): O(A) fx)--2x4 - 92x2 +294 -(B) f(x) =x4 + 52x2 + 147 (C) f(x) = 2x4 + 92x2-294 (D) f(x)--X 4-52x2-174 3. Find an equivalent expression for x2+49 +8x3- 125y3:. (A) (+7x-7+ (2x - 5y)(4x2+ 10xy+25y (B) (-70x-7)+(2x + 5y)y2x2- 10xy 5y (C) (x -7x - 7)+ (2x+ 5y)4x2-10xy 25y) (D) (x + 7)(x-7i) +(2x-5y)(4x 2 + 10xy + 25y 2) 4. Suppose A is a 4x 5 matrix and B is some other matrix. If we can successfully perform the multiplication AB, then which of the following is a possible set of dimensions for B? A)4x5 (B) 4 x 4 O(C) 5 x 8 (D) 12 x 4

Explanation / Answer

2) roots are ( - sqrt 3 , 0 ) and ( 7i , 0 )

passing through ( 1 , 200 )

polynomial function can be written as

f(x) = a ( x + sqrt 3 ) ( x- sqrt 3 ) ( x- 7i ) ( x+7i )

plugging 1, 200

200 = a (1 + sqrt 3 ) ( 1- sqrt 3 ) ( 1- 7i ) ( 1+ 7i )

a = -2

f(x) = -2 ( x + sqrt 3 ) ( x- sqrt 3 ) ( x- 7i ) ( x+7i )

f(x) = -2x^4 - 92x^2 + 294

option a is correct

2) x^2 + 49 + 8x^3 - 125 y^3

factoring x^2 + 49

( x + 7i ) ( x - 7i )

factoring 8x^3 - 125y^3

= ( 2x - 5y ) ( 4x^2 + 10xy + 25y^2 )

so the expression can be written as ( x + 7i ) ( x - 7i ) +  ( 2x - 5y ) ( 4x^2 + 10xy + 25y^2 )

option d is correct

3) if A = 4x5 matrix

then the inner dimension of B matrix has to be 5 inorder to successfully multiply

so dimension of B couls be 5X8

option c is correct

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