I. Solve using De Moivre's Theorem. Find the real values of the number "a" from w/c "ai" is a solution of the polynomial equation, x* – 2x3 + 7x² – 4x + 10 = 0, then find the roots of the equation

Q: Given this polynomial x²+3x+5=0 such that r and s are the two roots of the equation. Find the value…

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Q: If -5 is a root of the quadratic equation 2x2+px-15 = 0 and the quadratic equation p(x2+x)+k=0 has…

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Q: Find the values of k for which the equation x3+5kx+16=0 has no real roots

A: Given- x2+5kx+6=0 To Find- The value of k for the above quadratic equation has no real roots.…

Q: Find all the solutions to the polynomial: x* + 4x°+7x² + 16x + 12 = 0 1 -4 -2i O 2i -3 O -1

A: A polynomial function is a function that involves only non-negative integer powers or only positive…

Q: Use the quadratic formnula to solve for x. 4x*+8x+1=0

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Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A: For solving a polynomial equation put

Q: Use the Intermediate Value Theorem and Rolle’s Theorem to prove that the equation has exactly one…

A: In the given question, it is required to use Intermediate Value Theorem and Rolle’s Theorem.

Q: Find the roots for the quadratic equation x + 6x +9 = 0 A 4 B. 1 F 3 -3 D. -2 H. -1

A: The correct option is G.

Q: Show that the product of the roots of a quadratic equation is c/a .

A: Consider the quadratic equation ax2+bx+c=0 Also consider that α and β are the roots of the quadratic…

Q: 7.4x+4x3-2Sx2 -x+ 6 0 XI =-3

A: Since you have asked multiple questions, as per company guidelines we will solve the first question…

Q: Find the formula, in standard form y=ax2+bx+cy=ax2+bx+c, for a quadratic that has roots at x = -3…

A: We have to find a quadratic that has roots at x = -3 and x = -2, and has leading coefficient of 1.

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

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Q: Find the solutions of the quadratic by factoring. SHOW ALL OF YOUR WORK. 2.x-7x 15 = 0

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Q: State whether the given quadratic equations have two distinct real roots .Justify your answer  i)…

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Q: If -5 is a root of the quadratic equation 2x^2 +px-15=0o and the quadratic equation P(x^2 +x)+K=0…

A: GIVEN: 2x2 + px - 15 = 0              Root of this equation is -5

Q: 49 Find a quadratic equation with integer coefficients whose roots are the reciprocals of 4x2 - 23x…

A: We have to find a quadratic equation whose roots are reciprocal to roots of given equation- given…

Q: Find the roots of x+2x+5=0 by using quadratic formula.

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Q: Use the discriminant to determine the number and types of solutions of the quadratic equation. x2 -…

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Q: 4) a) Show that the equation y = x³ + 3x2 + 16 has exactly one real root. What is it

A: To show That the equation y=x^3+3x^2+16 has exactly one real root.

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

A: The detailed solution is given below Thank you

Q: B. Find a polynomial equation with integer coefficients that has the following roots. 1, -2, -5 1.…

A: Given that:                         1. 1, -2, -52. ±1, 23. ±2, ±3

Q: 1.Solve the following polynomial equations.  a)  2X2+1=x2+2X

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Q: 2. Solve the polynomial equation for all zeros. x4 + 5x2 =z?

A: Simplify the polynomial equation x4 + 5x2 = x3 as follows.

Q: Find the value of p so that the quadratic equation px (x-3) + 9=0 has two equal roots

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Q: Find the polynomial equation of lowest degree, with real coefficients and leading coefficient 1 that…

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Q: Find the roots of the quadratic function f(x) = 2x2- 6x + 7 by the method of completing the square.

A: Topic : quadratic equation

Q: Solve the roots of the equation f(x)=-0.5x^2+2.5x+4.5 a.With the Graphical Method b.Using…

A: Here, we need to find the roots of the equation f(x)=-0.5x2+2.5x+4.5. For (a), Graphical Method:…

Q: Solve for X, and check the extraneous roots. X/(X + 4) =11/(X2 -16) + 2/1

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Q: Use the quadratic formula to solve for x. 9x+ 5x–1=0 (If there is more than one solution, separate…

A: We have given equation 9x2+5x-1=0 Then, comparing this ax2+bx+c=0 we have a=9,b=5,c=-1 Now, using…

Q: Compute the value of the discriminant and give the number of real solutions of the quadratic…

A: Suppose ax2+bx+c = 0 is a quadratic equation. The discriminant of the quadratic equation is b2-4ac.…

Q: ). A polynomial equation whose roots are {-1, 1 and 7} is A. x - 7x2 -x-7 =0 B. x + 7x? – x -7=0 C.…

A: Given: To find a polynomial equation whose roots are {-1, 1 and 7}

Q: The function x- 2r-6x+22x – 15=0 has how many roots?

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Q: 29. Use the quadratic formula to find the roots of the following quadratic: y = 2x² – 11x + 5 -

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Q: Find the value of m so that the quadratic equation mx (x-7)+49 = 0 has two equal roots

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Q: 1. Use what you have learned to solve the following polynomial equation by either completing the…

A: To solve given polynomial equation: Here, By using the quadratic formula, ax2+bx+c=0 x = -b…

Q: Compute the value of the discriminant and give the number of real solutions of the quadratic ed 5x…

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Q: Find, in surd form, the range of values of m for which the quadratic equation: x* +(3-m)x+10=3 has…

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Q: Use the quadratic formula to solve forx. 5x+5x-1 0 (If there is more than one solution, separate…

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Q: b) Find all the roots of x3+7x²+7x+1%3D0

A: First find the one root by hit and trial method then using long division form the quadratic and…

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

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Q: Find the value of the constant "k": 3x^2-5x+ 4k-5-0 has one root equal to 0.

A: We will use formula for root of quadratic equation

Q: Solve the following polynomial equation by grouping and factoring. 4y^3−9y=0   Enter the exact…

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Q: 2.) × 1+2xー13x2- 14xt2イ=0

A: To find  The complete set of possible rational roots.

Q: 3. If x=-2 is one of the roots of 6x'+11x - 4x -4 = 0, find the other two roots of the polynomial…

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Q: Obtain the roots of the following equation by the fixed point method starting at x = 1 and solving…

A: To obtain the root of 4x2-2x-9=0 using fixed point method with x0=1

Q: Find the value of the discriminant and determine the number of real number solutions of the…

A: Topic = Quadratic equations Correct answer = 29 ; Two

Q: If a and 3 are the roots of the quadratic 3x2 – 4x + 6 = 0, find the value of

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Q: Show the work steps for finding the roots of x* – 13x² + 36 algebraically.

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Q: Choose the letter of the best answer. Write the chosen letter on a separate sheet of рaper. 1. What…

A: Consider the given equation 3x2+5x=6. The general form of a quadratic equation is ax2+bx+c=0, a≠0.…

Q: Find the roots of the polynomial equation. x3- 2x2 + 10x + 136 =0 Select one: O a.-3 + 5 i, -4 O b.…

A: Given,  A polynomial of degree 3 : x3 -2x2 + 10x + 136= 0