In the process of solving 2x3+7x2+9x+10=0, you test 1, 2, 5, and 10 as possible zeros and determine that none of them are actual zeros.  You then discover that  -5/2 is a zero and the quotient upon dividing by (x + 5/2) to be 2x2+2x+4.  Do you need to test 1, 2, 5, and 10 again?  Why or why not?

Q: 1. Discuss the possibilities for the roots to : 2x-5x -6x+4 = 0

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Q: From the given polynomials be able to solve each by %3D factoring or any other way of solving to…

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Q: The polynomial x(x^2-4)(x^2+4) has___ real roots.

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Q: The area of a rectangle is (x^2 + 8x + 12) cm^2. If the length of the rectangle is (x+6) cm, show…

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Q: 4. If x=-4 and x=1 are the roots of x* + 3x' - 3x +3x – 4 = 0, find the other two roots of the…

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Q: The roots of 6x² +7x + 34 = 0 are: Real and Equal Real and Distinct Complex and Unequal Imaginary…

A: These questions  are related to algebraic operations, we will solve it using given information.

Q: If x+3 is a factor of P(x)=3x^3+5x^2-11x+3, find the roots of P(x)

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Q: Show that the equation x4 + 4x + c = 0 has at most two real roots

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Q: 1. Find the quotient of x3 −5x2 −2x+ 24  by x−4, and then divide the quotient by x−3. What are the…

A: x-4x2-x-6x3-5x2-2x+24-x3∓4x2-x2-2x+24∓x2±4x-6x+24-6x+2400    ∴x3-5x-2x+24=x2-x-6 x-4 —∗…

Q: 4. x-2x+1= 3

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Q: Determine the set of values of k for which the equation (3-2k)x + (2k – 3)x+1 = 0 has no real roots.

A: For no real solution of quadratic equation, Discriminant (D) < 0

Q: Show that the equation e +-23D0 has no real root which is less than 1.

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Q: The polynomial x^5+x+7=0 has exactly one real root and how would I explain that this root must be…

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Q: 15. Given the equation 3x-4x -12 =0, how many roots are there? Rational or irrational?

A: Given equation  3x2-4x-12 = 0 ....... (1) Quadratic formula for the solution of the quadratic…

Q: (a) Factor (fx)=x^3-4x^2+x-4 into factors of the form (x-c), given that 4 is a zero. (b)…

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Q: From the given polynomials be able to solve each by factoring or any other way of solving to find…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: (a) Factor: x2-2x- 3 (b) What the roots of x2 - 2x - 3 = 0?

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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: I. Find the value of k so that the remainder in each division problem is (a) 21. (2x³ + 3x² + kx-2)…

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Q: Use the Intermediate Value Theorem to show that the equation                       x6 - 8x4 + l0x2 -…

A: To showx6-8x4+10x2-1=0 has atleast six distinct solutions using intermediate Value theorem.

Q: How many additional years of education are required to double your income?

A: In the given expression, 1.18x = 2 This can be solved by taking log both sides

Q: If -2 is a root of the equation x² + px - 6 = 0 and the equation x²- px + q = 0 and the equation x²-…

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Q: Solve for x. -8 -14 x-3

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Q: 12. If x=-1 is a root of x + 4x? -x -4 =0, use synthetic division to factor the polynomial…

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Q: What are all the roots of x5 – x4 – 3x3 + 3x2 – 4x + 4 = 0

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Q: 22. Solve the following for all solutions, both real and imaginary. f(x) = 2 x - 17x + 30x -8. Since…

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Q: To show that x = -3 is a solution of the given equation, divide f(x) = x -37x - 84 by (x + 3) using…

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Q: For what value of a will five of the six real roots of 6x6 + 7x5 _ 43z4 - 153 + 49z2 + ax polynomial…

A: For what value of a will five of the six roots of polynomial P(x) be shared by the polynomial Q(x)

Q: 1 for x. 2 Solve - x+1 -+ 5 =

A: The given equation is                                               2x+1+5=1x

Q: If [x² - 2x + a] = 0 has no solution, then find where [] represents the greatest integer).

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Q: Solve for x. 1 1 -2 -5 -4 =3 - 1 x=0 Q14 11.3

A: Please refer to the image below

Q: Show that the equation 6x4 – 7x +1 = 0 does not have more than two distinct real roots.

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Q: 7) Divide x2 - 4x + 11 by x - 3 Show to So Solve by What -( What 1). remainder.

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Q: How many positive integer solutions are there to x1 + x2 + x3 =15 ?

A: From the given information we want to find How many positive integer solutions are there to x1 + x2…

Q: what is the factored form of ax^2+bx+c where the roots are x1 and x2?

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Q: Show that the equation r1 + x³ + 4x – 2 = 0 has exactly one real root.

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Q: The product (x - 2)(x + 3) is positive if both factors are negative or if both factors are positive.…

A: Given: The inequation x-5x+8≤0, To find: The solution of the given inequation.

Q: What are all the possible rational roots of 2x³ + 3x² – 10x +4=0? 글 only A B +1, ±2 only +1, ± 2, ±…

A: Possible ration rational of any polynomial are ±Factors of constant termleading coeficient Therefore…

Q: The roots of x² + 4x + 7 are________. -real and rational -real and irrational -imaginary

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Q: What are all the possible rational roots of 2x^3 + 3x^2 - 10x + 4 = 0?

A: Given: - The equation is, 2x3+3x2-10x+4=0 To find: - The rational roots of the given equation.

Q: 1. Find how many real solutions x2 + 6x + 24 has. What are those solutions (real or otherwise)?

A: Since you have posted multiple questions as per our guidelines we are allowed to answer the first…

Q: One of the roots of the polynomial equation 2x^3 + 9x^2 - 33x + 14 = 0 is 2. Find the other roots. *…

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Q: of non-negative integer solutions to the  equation x1 + x2 + x3 + x4

A: Introduction: An integer that is neither positive nor negative is referred to as a non-negative…

Q: x to the third minus 512 over x-8 and must be solved using synthetic division.

A: First of all, consider the dividend and the divisor.

Q: Discuss the possibilities for the roots to : 2x'-5x - 6x+4 = 0 12. 3x - 5x -x² -8x+4 =0

A: We can use Descartes rule of signs to check the nature of possible roots of the given function, P(x)…

Q: Prove that one solution of the equation                               2.00x4 - 3.00x3 + 5.00x =…

A: Given equation is 2x4-3x3+5x=70 --- (1) To prove that  x = -2.22 is one of the solution of the above…

Q: If 1 is one root of the equation kx⁴ + (2k + 5)x³ + (3 – k) = 0, then the value of k is   A. 1 B. -4…

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Q: To find the possible roots of the polynomial 4x3 + x4 - 7x² - 8x - 8

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Q: find the roots x^4-4x^3+8x^2-8x+4=0

A: To find the roots.x4-4x3+8x2-8x+4=0

Polynomials

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