If f(x)= 10x -37x+11, then there are two real numbers a

Q: Find two positive real numbers x and y such that they add to 120 and x2y is as large as possible.

A: Oue Aim is to find two positive real nnumbe x and y such that theyadd to 120 and x2y is as large as…

Q: Find k such that f(x) = x3 - kx2 + kx + 2 has the factor x - 2.

A: The general polynomial equation of degree n  is an equation of the form…

Q: if y3-3ax2+x3=0,then prove that y2+ 2a2x2y-5=0

A: Let dy/dx= y1 and d2/dx2=y2 And We will use the product rule of differentiation.

Q: Show that x3 +x – 1 has a root in the interval [0,1]. (R

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Q: Show that f(x) = x3 - 2x - 1 has a real zero between 1 and 2.

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Q: Find two positive real numbers such that they add to 40 and their product is as large as possible.

A: Our Aim is to find two positive real numbers a and b such that they add to 40 and their product is…

Q: The function f(x) = x -x2 - x- is graphed in 11 %3D 4 the xy-plane above. If k is a constant such…

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Q: Show that Y1 = X1/X2 and Y2 = X1 + X2 are independent and that Y2 isχ2(r1 + r2).

A: Given Y1=X1X2Y2=X1+X2

Q: Give an expression for f(x) of degree 3 with roots z = -4 and r = -2, where the root at r = -2 has…

A: Zeroes are x=-4 and x=-2and x=-2 has multiplicity 2

Q: Show that the equation x-4y+7z=14 , 3x+8y-2z=12 , 7x-8y+26z=5 are not consistent

A: Show that the equation x-4y+7z=14 , 3x+8y-2z=12 , 7x-8y+26z=5 are not consistent  We use Cramer's…

Q: f(x)=x^3-18x^2+105x-197 For what numbers does ff have a critical number?

A: To find the critical number of a function f(x) , set  f '(x)=0 and then solve for x.

Q: A chemical manufacturer wants to lease a fleet of 28 railroad tank cars with a combined carrying…

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Q: if y3-3ax2+x3=0 ,then prove that y2+2a2x2y-5=0

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Q: The domain off(x) = 3-x is 1-x2 %3D 1. R 2. R/{1,-1} 3. R/{3} 4. (0, ∞)

A: Domain: The domain of a function is the set of all input values for which the function is defined.…

Q: Find all solutions of x2 - x + 2 = 0 over Z3[i].

A: Given: Z3i=a+bi|a,b∈Z3       =0, 1, 2, i, 1+i, 2+i, 2i, 1+2i, 2+2i We have to find all solutions for…

Q: Find an equation of polynomial function with real coefficients having zeros at 3,-1,4+2i

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Q: If f(x) = 3x — 7, find the image of 2 and the preimage of 2

A: Given: fx=3x-7 To determine: Image & pre-image of 2.

Q: Find an nth-degree polynomial function with real coefficients satisfying the given conditions as : n…

A: Since 1 and i are the zeroes of the polynomial, therefore

Q: Find the constant a, such that the function is continuous on the entire real line. f(x) = {2x2,…

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Q: Show that f(x) = x5-x3-1 has at least one real zero between 1 and 2.

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Q: Let h(x) z² –3z+2 -z² –4x+4' what is h' (-5)?

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Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y -5=0

A: Our objective is to prove y2 + 2a2 x2 y -5=0 if  y3 -3ax2 +x3 =0. But note that when a=0 and x, y=3,…

Q: How does the linear factorization of f(x), that is, AX)=an (x-c1)(x-c2) (x-C). show that a…

A: Here the linear factorization of the function f(x) is given as:…

Q: If X is a positive number such that : X² – 10X = 9VX Then X – VX = ?

A: given:x2-10x=9xsquaring both the sides:x4-20x3+100x2=81xwe get x=0, x=1, x=19±372.but for the…

Q: Prove that f (x) = x3 + 3x2 + 6x has precisely one real root.

A: Number of real zeros of a quadratic equation can be determined using its discriminant. For a…

Q: If f(x) <0 for all real numbers x then f is decreasing or increasing on its interval?

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Q: 2 is > 2 of x, the

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Q: Prove x²(x-y)² =x² -y²

A: Substitute x=y in the given equation Then x2(x-y)2=0 ....... (1) and x2-y2=0 ....... (2)

Q: Does f(x) = x - x - 5 have a real zero between 1 and 2? %3D

A: f(x)=x3-x-5 have a zero between 1 and 2.

Q: Prove that there exists a unique real number solution to the equationx +x² – 1 = 0 between x = 2/3…

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Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y-5=0

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Q: if y3 -3ax2 +x3 =0,then prove that y2 + 2a2 x2 y-5 =0

A: Given : y^3 - 3ax^2 + x^3 = 0

Q: If y3-3ax2+x3=0,then prove that y2+2a2x2y-5=0

A: Solution of this question is

Q: Investigate the based on linearization 3 x = x₁ - x₁²³²+x₂z xr 394 - 292 6 Ac

A: This is a question of equilibrium and stability.

Q: (a) Show that (x2 + v2x + 1)(x² – v2x + 1) = x* + 1.

A: Given that: (x2+2x+1)(x2-2x+1)   NOTE: As per our answering guidelines, we can only answer 1…

Q: Use Cramer's Rule to solve for x2. xi + 2x2 +x3 = 2 3x1 – x2 - 2x3 = 7 X2 +x3 = -1

A: Here we have given one matrix and we have to find the value of x2 by using the Cremer’s rule.   Now…

Q: Use calculus to find the critical number of f(x)= x4/4 - x3/3 -3x2+10

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Q: Prove that f(x)=4x-2^2x has at least one real zero in the interval [1,2] without actually solving…

A: The given data is: Prove that fx=4x-22x has at least one real zero in the interval 1,2 without…

Q: If f'(x) has no roots, then f (x) has exactly one root. If f (x) has three roots, then f'(x) has at…

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Q: Among all pairs of numbers (x, y) such that 2x +y = 9, find the pair for which the sum of squares, x…

A: NOTE: Refresh your page if you can't see any equations. . the given constraint is

Q: 2. Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x=…

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Q: Find the sum of all the critical numbers of f(x) = 2x3 +3x2 – 36x +8 -

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Q: The total number of passengers riding a certain city bus during the morning shift is 900. If the…

A: Let x be the number of children and y be the number of adults. Given that, the total number of…

Q: (i) Show that f(x) = 6x³ – 2x2 + 4x – 3 has exactly one real root. (j) Show that f (r) = x + 2x5 +…

A: Given: i. fx=6x3-2x2+4x-3ii. fx=x7+2x5+3x3+14x+1 To Show: Given equation has exactly one real roots.…

Q: Find two positive real numbers x and y such that they add to 123 and  x2y  is as large as possible.…

A: We have to find out x and y

Q: ) Show that |2x - 2|-|x+1| +2≥0 for every x € R.

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Q: Prove that the equation x- 15x +k = 0 has at most one root in the interval [-2, 2]. Hint: You'll…

A: Dear friend,  if you have any other query about this problem, then please tell me about your query I…

Q: Show that x^2 + 1/x^2 is greater than or equal to 2.

A: A.M  is greater than or equal to G.M

Q: Find critical number of g(x) = x^2 - 8x +9

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Polynomials

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