What is/are the value/s of k in the quadratic equation 2x² – 5x – k = 0 whose roots are imaginary? A. k< B. k<- C. k>-5 D. k> O A Ов O D

Q: Which quadratic equation has roots 2 + 6i and 2 – 6i? x2 – 4x + 13 = 0 O x2 + 4x + 13 = 0 Submit…

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Q: Use the proof by cases to prove that there are no solutions in integers x and y to the equation 4x?…

A: Here we use the fact that x2≥0 and y2≥0 and will be square of some integers. So possible values of…

Q: Determine the all the roots of z4 +1 = 0

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Q: 7. Which of the following most precisely describes the roots of the equation 3x2 + 4x-1 0?

A: We first compare the given equation with ax2+bx+c=0  so, a=3, b=4, c=-1 The discriminant for the…

Q: If the roots of   (1+m)x2-2(1+3m)x+(1+3m)=0 are equal then find the value of m

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Q: Use the quadratic formula to solve for x. 2x+8x= -1 Round your answer to the nearest hundredth. If…

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Q: 3. Use Graeffe's Root Squaring Method to de the real roots of the polynomial equation х3 + За? — 6х…

A: GRAEFFE'S ROOT SQUARING METHOD:   The roots of any polynomial equation with real coefficients can be…

Q: Solve 0 = x2 - 10x + 30 by completing the square. O A. x 5+i and x = 5 -i O B. x = 5 + iv5 and x = 5…

A: Solution: The objective is to solve the given quadratic equation by completing the square

Q: 4. What are the roots of the quadratic function y =-x +3x-4? A x+1 and x=-4 x--1 and x-4 315i 3 7 3…

A: Shri Dharacharya method is to be used here

Q: Use the quadratic formula to solve for x. 2x-2x-1=0 (If there is more than one solution, separate…

A: The general quadratic equation is of the form ax2+bx+c=0, where a, b and c are the coefficients. The…

Q: Use the quadratic formula to solve for x. 3x-9x=-4 Round your answer to the nearest hundredth. If…

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Q: Find the root(s) of the quadratic equation O(4. -5) O (2. 6) O (-2, -3) O (1. 5) -6x +5 0

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Q: show that 1+i is a root of the cubic equation 3z^3-5z^2+27z-45=0, find the other two roots

A: 3z3-5z2+27z-45 = 0Using rational root test :±11, ±13, ±31, ±51, ±91, ±93, ±151, ±153, ±451,…

Q: 14. The condition for the quadratic cquation x2 + 2kx + (k + 6) = 0 to have two uncqual real roots…

A: When a quadratic equation have two real unequal real roots then the value of discriminate is greater…

Q: Find all the values of m such that the equation mx² – 2 (m + 2) x + m + 2 = 0 has two real roots

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Q: This question must be solved by "the quadratic formula". Be sure to show your work accordingly. 2-…

A: The quadratic formula for the quadratic equation ax2+bx+c=0 for finding roots is given by,…

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: If the roots of the equation x2+2cx+ab=0 are real unequal,prove that the equation…

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Q: 10.) Solve for both roots in the following equations using the quadratic formula where az^2+ bz +c =…

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Q: 12. For what values of k, will the equation 3x? +4x + k = 0 have two equal roots?

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Q: 11. Without solving, determine the number of real solutions for each quadratic equation. Show work.…

A: Given:- a) 5q²-3q-6=0 b) 3y²-5y +9=0  To find:- Number of real roots of given quadratic equations

Q: Assume that P and Q are two positive distinct real roots of the quadratic equation (²₂. - -…

A: given quadratic equation t2-P+Qt+PQ=0 here assume that P and Q are two positive distinct roots of…

Q: The sum of the roots of 2x+10x² -4x+5=0 is 5 0 .a O None of these b o -5°C 0 d o

A: Given,          The equation is 2x4+10x2-4x+5=0.

Q: What are the roots of the equation ² - 5x 2 0? 5 V17 2 -5 V17 2. (1) x = (3) x = (2) x = 5 33 2 (4)…

A: given,

Q: Give the general solution to the HLDE with the given set of auxiliary roots. m = 0, 3, -1, l±/2 m…

A: Solution is given as below:

Q: How many positive real roots are there in the equation 7x²+5x+3x²+x=0? a. 2 b. 0 C 3 a. 144 b.…

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

Q: #7 using Descartes's rule of sign

A: Part (a) The polynomial f(x) = x3 +3x +7 has a degree 3, so, it has 3 roots. For positive real…

Q: If the roots of equation x² - 2cx + ab = 0 are real and unequal, - then prove that the roots of x²…

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Q: (a) If Q: R"R is a quadratic form, ex that O takes on

A: Given, Q : ℝn→ℝ is a quadratic from,

Q: - (b) Without extracting the roots, determine which one is greater, VII-5 or, 19 – /13.

A: Solution

Q: 6. Show that the quadratic equation ax² + b – a = 0 (a± 0) has two distinct real roots.

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Q: 27. Find the exact solutions and simplify as much as possible: 3x = 6x + 2. Show work.

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Q: Suppose a quadratic equation is given as follows: (k – 1)x² + x + 1 = 0 Select all values of k for…

A: k-1x2+x+1=0 The Formula for discriminant is- D=-b±b2-4ac2a

Q: What are the imaginary roots of the function in #20? f (r) = x³ + 2x2 + + 3x + 6

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Q: If the roots of equation x² - 2cx + ab = 0 are real and unequal, then prove that the roots of x²…

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Q: If the roots of the equation x2+2cx+ab=0 are real unequal ,prove that the equation…

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Q: Let A and B be real numbers such that a root of the equation z ^ 3 + Az ^ 2 + Bz + 26 = 0 is 1 + i.…

A: First of all, as coefficients A and B are real, we know that, if z ∈ C is a root of an equation,…

Q: Advanced Math Question

A: To answer the given question we shall use the following rule. Descartes' Rule: The number of…

Q: 3. Let 7, r, and r, be the roots ofx' +3x-5x-4= 0, construct the equation whose roots are: 7(r, +r3…

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Q: Whatis the value of r in the quadratic equation x² – 10x – r = 0 whose roots are equal rational and…

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Q: 4. Which of the qundratic equation has no real roots? 1. x*+ 3x - 10 -0 5 Whnt is the nature of…

A: The equation ax2 +bx+c= 0 has real roots if b2 -4ac=0

Q: How many real-number solutions are there to the quadratic equation 2x2 + 5x + 1 = 02 a. eslim b. 1…

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Q: (4) Show that in general, the sum of the roots of a quadratic equation ax? + bx + c = 0 is whereas…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: According to Descartes's rule of sign, how many possible positive and negative roots are there for…

A: Answer is  3 positive roots  And 1 negative root. Explanation is given below..

Q: (4) Show that in general, the sum of the roots of a quadratic equation ax² + bx + c = 0 whereas the…

A: See the attachment

Q: Which quadratic equation has irrational roots? 2? + 7а — 30 — 0 2? + За — 40 — 0 - x2 – 11x + 18 = 0…

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Q: If one of the roots of ax^2 + bx + c is 2/3 + 5/9i where a, b and c are integers, what is the value…

A: Explanation of the answer is as follows

Q: Show that the equation has exactly one real root. 25 + 6x + 7x^5 + 4x^7

A: Given equation is    25+6x+7x5+4x7   First if we look at the limits of our function we see, that:…

Q: B. Give the general solution to the HLDE with the given set of auxiliary roots. 2. m =-2, -2, 5, 5,…

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Q: Given that the equation z2 + (p + iq)z + r + is = 0, where p, q, r, s are real and non-zero has a…

A: Introduction :--