if the sum of the zeroes of the polynomial f(x) = 2x³ – 3kx² + 4x - 5 is 6, then the value of k is

Q: Given that one of the zeroes of the cubic polynomial ax3+bx2+cx+d is zero , the product of the other…

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Q: quadratic

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Q: if sum of the squarew zeroes of the quadratic polynomials  f(x) =x2-8x+k is 40.Find K

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Q: Solve the problem. 11) Find a polynomial for the perimeter of the rectangle. (4x + 6) units - X +…

A: The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle we have…

Q: If sum of the squares zeroes of the quadratic polynomial f(x) =x2-8x+k is 40.Find k

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Q: Find the roots of the quadratic polynomials: f (x) = 4x2 − 3x − 1

A: Given f (x) = 4x2 − 3x − 1

Q: 4. The polynomial equation whose roots are {-1, - ½ and 3} is А. 2х3- Зx2 - 8х-3%3D0 В. х3 - 6х2 - х…

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Q: if the sum of squares zeros of the quadratic polynomial f(x) =x^2-8x+k is 40. Find k

A: If the roots of ax2+bx+c=0 are m and n Then m+n=b, mn=c

Q: If the sum of the squares zeros of the quadratic polynomial f(x) =x2-8x+k is 40 .Find k

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Q: Find the quadratic polynomial if the zeroes of it are 2 and 1/3 respectively.

A: Find the quadratic polynomial

Q: If the sum of the zeroes of the polynomial p(x) = (k2 -14) x2 - 2x -12 is 1 . Then find the value of…

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Q: Find the remainder when f(x) = x7 + 3x5 + x - 1 is divided by x2 +1 in Z5[x].

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Q: Find the condition which must be satisfied by the coefficients of the polynomial f(x)=x3-px2+qx-r…

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Q: If sum of the squares of the zeros of the quadratic polynomial f(x ) =x2-8x+k is 40,find the value…

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Q: Find the value of k in the given polynomial if one of the zeroes is -3  (k-1)x2+kx+1

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Q: 4x

A: Zeros of f(x) must satisfy f(x),i.e., f(x) will reduce to zero at the zeros of f(x).

Q: Find the leading term of the polynomial function. f(x) = 3x45x² + 3x - 8 0x4 3 8 3x4

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Q: The number of zeros of the polynomial x² + 3x + 2 in Z, is: 4 2 1 None

A: The polynomial is given as f(x)=x2+3x+2 Z6=0,1,2,3,4,5

Q: Prove that x- 3 is a factor of the polynomial x + 4x-17x2-14x + 6 without referring to the graph.

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Q: Find the zeros of the polynomials f(x) =x2 -5x2 -16x +80 ,if it's two zeros are equal in magnitude…

A: The answer is given below:

Q: If the remainder on dividing the polynomial 2x* – kx +5x-3k+3 by (x + 2) is 4, then find the value…

A: Use the given information.

Q: If one of the zeroes of the quadratic polynomial (k-1)x2+kx+1 is - 3 then find the value of k

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Q: one of the zero of the quadratic polynomial f(x)=4x2-8kx-9 is negative of the other , then find the…

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Q: If one of the zeroes of the quadratic polynomial f(x) = 4x2 - 8kx - 9 is equal in magnitude but…

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Q: One factor of f(x) = x^3 –8x^2 – 15x+54 is x - 2. What are the zeros of f(x)?

A: Solution of the equation

Q: The profit function, in dollars, for a product is given byΠ(x) = −x^3 + 76x^2 − 380x − 2800,where x…

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Q: Find the value of p from the polynomial  x2 +3x+p if one of the zeroes of the polynomial is 2

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Q: Find a polynomial of degree four that has zeros -3, 0, 1, and 5, and the coefficient of x3 is -6.

A: We need to find a polynomial of degree four that has zeros -3, 0, 1, and 5, and the coefficient of…

Q: The term containing the highest power of x in the polynomial f (x) is 6x. One of the roots of the…

A: Given the quadratic polynomial x2-2x+3 is a factor of f(x) and the highest power of f(x) = 3 Let…

Q: Suppose p(x) is a cubic polynomial that shares two of its roots with f (x)=2x² – 5x+3, has the same…

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Q: The number of zeros of the polynomial x^2 +4x+1 in Z6 is:

A: See the detailed solution below.

Q: if the sum of squares zeros of the quadratic polynomial f(X) =x2-8x+k is 40.Find k

A: We can find the value of k as below

Q: Find all zeros of polynomial  P(x) = 3x^3+x^2+7x-6

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Q: Find the quadratic polynomial whose graph goes through the points (-2,8), (0, 6), and (1, 11). f(x)…

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Q: If sum of the squares  zeroes of the quadratic polynomial         f(x)=x2-8x+k is 40 . Find k

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Q: For a polynomial equation P(x) = 0, if P(x) is not factorable, then P(x) = 0 has no real roots.…

A: For a polynomial equation P(x) = 0, if P(x) is not factorable, then P(x) = 0 has no real roots.

Q: Find the value of k in the given polynomial if one of the zeroes is - 3  (k-1)x2+kx+1

A: The given function is  f(x) = (k-1)*x2 + kx +1

Q: Find the zeros of f(x) = 3x^3 + 9x^2 + x + 3

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Q: If one of the zeroes of quadratic polynomial (k-1)x2 +kx+1 is - 3 then find the value of k

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Q: Find the quadratic polynomial whose graph goes through the points (-1, 3), (0, 1), and (1,7). f(x) =

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Q: 8. Find the sum of all the zeros of the polynomial f(x) = x + 2x2-5x-6 O -5 -2 0. 2 6

A: Given equation is fx = x3+2x2-5x-6Comparing it with ax3+bx2+cx+d = 0a = 1, b = 2, c = -5, d = -6

Q: Find the third degree polynomial function that has an output of 40 when x=1, and has zeros −19 and…

A: Here we need to find cubic polynomial with complex zeros x=-i, x=-19

Q: find the maximum number of real zeroes of the polynomial  f(x)=-2x7-3x8-6-5x5

A: Given by f(x)=-2x7-3x8-6-5x5 f(-x) = 2 x^7 – 3 x^8 –6 + 5x^5 There are  three changes s, three…

Q: Find a polynomial f (x) of degree 4 that has the following zeros. -4, 1, -9, 0 Leave your answer in…

A: Polynomial  with zeros -4,1,-9,0 can be written as below :

Q: Write an equation for a polynomial that has four turning points, end behavior of up and down, and…

A: A polynomial with an nth degree has n number of roots. The end behaviour of the graph is how the…

Q: The graph of the polynomial function f(x) = −2x(x − 1)²(x − 2)² extends from

A: Given polynomial f(x)=-2x(x-1)2(x-2)2

Q: Find the critical points, A and B, of the following polynomial (with A<B) f(x) = 6x3 - 45x2 - 432x…

A: A = -3.04 B = 8.04

Q: Find the third degree polynomial function that has zeros -10 and -12i, and a value of 1,776 when x=2

A:

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.