Do all polynomial equations have at least one imaginary root?

Q: How many zeros can a quadratic function have?

A: We have seen that a quadratic polynomial is of the form: fx=ax2+bx+c ,a≠0 We assume that a, b and c…

Q: If a + bi is a root of a polynomial equation with real coefficients, b + 0, then. equation. is also…

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Q: Find a fourth degree polynomial with real coefficients that has zeros of -3, 2, i that passes…

A: Let us consider a fourth-degree polynomial:

Q: Give a POLYNOMIAL EQUATION with integral coefficients that has the following roots. Write your…

A: It is a fourth degree polynomial as we are having four roots.

Q: must every polynomial equation with real coefficients of degree 3 have at least one real root? Why

A: Recall: Fundamental theorem of Algebra: Any polynomial of degree n with real coefficient has n…

Q: The quotient rule for square roots states that if a and be are nonnegative and b doesn't equal…

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Q: Which quadratic function in vertex form can be represented by the graph that has a vertex at(4,-8)…

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Q: What are the real root(s) of the quadratic equation whose related function is graphed below? A (3,0)…

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Q: Write the equation of a third degree polynomial in standard form (multiply out) with the given…

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Q: Obtain all four roots of the equation = ++-0, and then express * +4 as product of quadratic factors…

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Q: Find the quadratic polynomial whose graph passes through the points (1, 3), (2, 17), (3,37). y =

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Q: Find the quadratic polynomial whose graph passes through the points (1, –6), (2,0), (3, 8). ||

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Q: Find a fourth degree polynomial that has zeros of 3,-3,i

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Q: Write a quadratic equation in standard form with roots -7/3 and 2 passing through the point (0,28).…

A: Quadratic equations  with roots p,q  y=a(x-p)(x-q)  Standard form of quadratic equation y=ax2+bx+c

Q: Determine the maximum number of real roots and possible real roots of the following polynomial…

A: We know that, a polynomial equation of degree n has maximum n roots.  If a+ib is a root of a…

Q: Complete the quadratic polynomial by filling in the number that makes it a perfect-square. x² +18x+

A: x2+18x+__ Let __ =nx2+18x+nn=?

Q: I have a question about roots. How quickly can you determine the number of roots a polynomial will…

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Q: Determine the number of real solutions using the quadratic equation. 101010101010101011…

A: Given problem:- 2n2-10n-8=0 To find:- number of real solutions of given quadratic equation

Q: How  many roots does the polynomial have?

A: NOTE: Refresh your page if you can't see any equations. . to find the roots, take P=0

Q: show that the equation x^5+2x^3+3x-4=0 has exactly one root. Justify your answer.

A: Given equation has only one root. Here is its explanation.

Q: Find the quadratic polynomial whose zeroes are -3 and 4

A: Solution:- We know that a quadratic polynomial can be written in the form of P(x) =x2 - (α + β)x +…

Q: Determine the roots of the auxiliary equation of 3

A: Given,            y'''+3y''-4y'-12y=0

Q: Write a fifth-degree polynomial in factored form that approaches positive infinity as x approaches…

A: Please refer the attached image for complete solution. THANK YOU.

Q: State the Zeros Theorem.

A: Statement: Let P(x) is a polynomial with integer coefficients. Let p/q is a zero of P(x) Then p is a…

Q: Find the roots of -x3 + 9x2 -18x = 0

A: Solution: The objective is to find the roots of the given equation

Q: Find a formula for the polynomial of least degree that is graphed below.

A: Given: To Find: The formula for the least degree of the above graph.

Q: Give a polynomial equation with integral coefficients that has the following roots. 0, -3, -1, 2

A: This question is related to polynomials, we will solve it using given information.

Q: . Find a polynomial of degree 3 whose zeros are -4, -1, 2 and y intercept 16.

A: Since you have asked multiple question, we will solve the first question for you. If youw want any…

Q: 4) -3, -4, 5 ansurer -2 -3 3 answer 6) - answer .

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Q: Simplify and write the resulting polynomial in standard form and indicate its degree. (8x2 + 7x - 5)…

A: Simplify and write the resulting polynomial in standard form and indicate its degree. (8x2 + 7x - 5)…

Q: What is a polynomial equation? When is it in standard form?

A: Solution: Polynomial Equation: The equation that involves variable (single independent), exponents,…

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: Assume the least square equation is ŷ = 10+20X. What does the value of 10 in the equation indicate?

A: Given: least square equation  ŷ = 10+20X Value of 10 in equation = ?

Q: Create a polynomial equation with real coefficients that has 2 and 1-i as roots.

A: To create a polynomial equation with real coefficients that has 2 and 1-i as roots.

Q: Pose a real-life problem that requires to solve a degree 3 polynomial equation. Solve the problem.

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Q: What is the largest value of the quadratic f

A: Here is the solution of the given problem.

Q: Is there a real number ______ whose square is -1? b. Does there exist _____ such that x 2 = −1?

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Q: Use a graphing device to find all real solutions of the equation. x5 = x + 3

A: Here given equation x5 = x + 3 Now let fx=x5,gx=x+3

Q: What is the maximum number of x-intercepts that a polynomial of degree 8 can have? The maximum…

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Q: If a + bi is a root of a polynomial equation with real coefficients, b ≠ 0, then________ is also a…

A: Given: if a+bi is the root of a polynomial equation with real coefficients,b≠0, then ..............…

Q: Determine a positive real root of this equation using appropriate software: 2x3 − 10x0.5 − 3x = −3

A: Consider the given equation as 2x3-10x0.5-3x=-3

Q: Explain how to determine the number and type of roots (both real and imaginary) from the…

A: Consider a quadratic equation, ax2+bx+c=0 The discriminant D of a quadratic equation can be defined…

Q: An equation with real coeticients has (-0, 3, and 4 among its roots. What is the lonest possible…

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Q: Write the rule of the cubic polynomial with roots 5, -2, and 0 that passes through the point (3,–7).

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Q: If the discriminant of a quadratic equation is greater than zero, the roots of the equation are:…

A: The polynomial equation whose highest degree is two is called a quadratic equation. The discriminant…

Q: Create an equation for a polynomial whose roots are x = -1, -5, 3 with a y intercept of 8.

A: Given :   Roots : x= -1, -5, 3

Q: Which is the cubic polynomial in standard form with roots 3, -6, and 0?

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Q: What is the degree of a polynomial equation? What are polynomial equations of degree 1 and degree 2,…

A: given , to define degree of polynomial equation and what are polynomial equations of degree 1 and 2

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.