24. Use the value of the discriminant to determine the number and type of roots of 2x -7x +9= 0- complex: imaginary rational: can be expressed as a fraction irrational: can not be expressed as a fraction a. 2 real, rational solutions b. 2 real, irrational solutions c. 1 real, irrational solution d. 2 complex solutions

Q: (ii) z + 7' = 2

A: I am providing the solution of (ii) only.

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: 7. Evaluate jir de 1 2 + 2x2 Solution;

A: Topic:- definite integration  Note:- as per our guideline if more than one question uploaded than…

Q: Let z, and z, be roots of the equation z² + pz + q = 0, where the coefficients p and q may be…

A: Given: Let z1 and z2 be the roots of the equation z2+pz+q=0, where the coefficients p and q may be…

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

A:

Q: 2. Prove: If ax? + bx + c factors nicely (i.e. the roots are fractions without square roots…

A:

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: Number 1a

A: Given cubic equation is,

Q: Which lists the possible types of roots for f(x) = 3x4 + 7a + 222 + + 9? Three complex roots and one…

A: Irrational and complex roots always exist in pair.

Q: Expand (x + 4)(x – 5) and use this answer to write down the quadratic equation in the form ax2 + bx…

A:

Q: Given that 1 is a double root of q (x)=D4x4-15x3+16x2_ 3x-2, find all roots. All the roots of q (x)…

A:

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: Given that z=1+2i and z=1-2i are roots to polynomial 2z^3-5z^2-cz-5=D0, where ER find the other root…

A:

Q: Show that this equation has a solution within [1,2] ?? Please indicate what theorem you are using.…

A: f(x) = xln(3x)−3 a = 1 b = 2

Q: quadratic equation

A:

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: 19. Find the exact solutions and simplify as much as possible: 2x2 + 9 = 12x. Show work.

A: Given equation:

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…

A:

Q: Which of the following representations of a quadratic has complex roots? Oal 9x2 + 33 = 0 b) -2.5 -2…

A: Hello! Thank you for the question but as per our honor code, we'll able to solve only three subparts…

Q: Let r, r, and r, be the roots of x’ +3x² –5x-4=0, construct the equation whose roots are: 7 (r, +r,…

A:

Q: 25. Use the value of the discriminant to determine the number roots of 2 + 20 = 12x - 16. complex:…

A:

Q: Answer the following: 1. Characterize the roots of the following quadratic equations using the…

A:

Q: Use the value of the discriminant to determine the number and type of roots of 2,2 – 7z + 9 = 0-…

A: Consider the equation, 2x2-7x+9=0 On comparing with the general equation ax2+bx+c=0, the value of…

Q: What are all the possible rational roots of 2r'+3x-10r +4=0? +1, + 2, +4 only +1, ± 2, t 4, only ±늑…

A:

Q: 4. Find the real roots of the following rational equations. x+7 X-3 %3D x-5 x+8 X-11 2х-22 618

A:

Q: Identify the case of the complementary solution: 49y" — 126у' + 102у %3D 0 - Select one: O a. Case 1…

A:

Q: What are the roots of x*-25? x= + 5, x = ± 5i %3D B x= + /5 only C. x = ± /5, x= ±i/5 %3D D…

A: using identities

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

A:

Q: a. Suppose that r E Q and r E Qª. Prove or disprove: The number (r – x)-1 e Qª. b. Prove or…

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

Q: 7.) What is the nature of the roots for y = 2x – 5? Use the discriminant to determine the nature of…

A: Given:- y = 2x2-5 To find :- Use discriminant determine the nature of roots

Q: 1. Find the discriminat -4ac, and the determine whether one real-number solution, two different…

A:

Q: Now we can finish determining det(A – AI). (Hint: To factor the cubic expression in the last step,…

A: We have to find the characteristic polynomial: 1-λ023-1-λ3201-λ

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: 2. Use successive substitution to determine the roots of 2x² + 5xy = 25 x + xy = 30 Initiate the…

A: Solution :-

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

A:

Q: What is rhe third root of unity ?

A: This question can be solved using the concept of complex numbers.

Q: Advanced Math Question

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

Q: Prove that the equation a3 – 4.x + 2 = 0 has three irrational solutions. Hin %3D but just show that…

A:

Q: 4. Find the roots of the following over C (a) x2 + 18x + 97 (b) x3 +3x2 - 6x -8 yes that is a cubic…

A: a)  x2+18x+97 Using the formula, x=-b±b2-4ac2a x=-18±324-3882x=-18±-642x=-18±i82x=-9±4i   c)…

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

A: .

Q: Show that if r is a rational number, then 2r2+3r+ 1 is rational as well.

A:

Q: 7.For which value of k will the roots of 2x + kox+1 = 0 be real? .2 1) 1 2) 2 3) 3

A:

Q: 10. What pair of factors should be used to find the complex solutions for x? 49x+36 0 (6x-71)(6x+ 7)…

A: In this question we have to find the complex roots of the given equation

Q: 2. Given that x4 −2x3 −7x2 +8x+12 = 0 has the roots −1 and 2, find the quadratic equation whose…

A:

Q: Given that -1 +5i is a complex root of the cubic polynomial x³+ 22x - 52, determine the other two…

A: Solution is here

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

A: Using quadratic formula

Q: 2. Isabel believes that f(x) = x3 - 9x2 + 27x - 27 has 3 complex roots. Nicky told her that it has 4…

A: Here we will use some basic results.

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 :--