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

Q: E A. by extracting square roots. 4. (x - 2)2 = 16 1. x2 = 169 5. 2(t - 3)2 – 72 = 0 2. 9b2 = 25 3.…

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Q: 1. Express the sum 2.019+2.020 into a fraction of two natural numbers. (2.019 = 2.019191919.. .) 2.…

A: As per the guidelines we can solve 1 problem only.

Q: 1 1. Solve the rational equation x - x - 6 x- 3 x +2 and state any NPV's.

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Q: 11. Solve the initial condition problem: f"(x) = 60x³ + 24x², f(2)= 239, f(-3) = 254

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Q: 4. Find all the solutions x of 1 Ax 1 ||

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Q: Solve the following quadratic for x: -6(x-12)(x+9) = 0 %3D O x = -6 and x = 21 O x = 12 and x = -9 O…

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Q: Find a quadratic equation whose product of roots x, and x₂ is X₂ equal to 4 and satisfying the…

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Q: Solve for z. 21 27 x-3 x-1

A: Here, we have to use the properties of similar trapezoids. If ABCD and CDEF are similar trapezoids…

Q: Show that the equation x - 17x + c = 0 has at most one root in the interval [-2, 2].

A: Any function y = f(x) will have exactly one real root in an interval if the function is either…

Q: (i) Given that x+ 2kx + 4k - 3 = 0 has no real roots, show that k satisfies k- 4k + 3 <0. (ii) Solve…

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Q: What is/are the value/s of k if the roots of X2 + x + k = 4 are equal?

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Q: Prove that for integers y=1 the equation 3h-n (2x₁ + x₂ + 4x₂) +3² (~1(2x₁+x₂+.+xn-1)+...+3^-1 (2²₁)…

A: We will use contradiction to prove it.

Q: (2) Determine k such kx - 4x+ = 0 that has real and different solutions. 2 %3D

A: Note: We'll answer the second question since the 2nd one is specified. Please submit a new question…

Q: would you prove that the answers to the diophantine equation y^2-x^3=0 are the pairs (n^2,n^3) for…

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Q: on 15 e quadratic approximation of the function f (x) =5x³– 4x+ 12 at x=1 is: P 15x2 – 19x+ 17 P…

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Q: 10. Write the sustem of lineor equations in the form Arebuand solve this motrit equat 2と, X, t Xu-9…

A: Given: 2x1  -x2 +x4 =93x2 -x3 -x4 =-9x1 +x3 -3x4 =-2x1 +x2 +2x3 =0 To find : x1x2x3x4 for system of…

Q: x2+Kx+64=0 & x2-8x+k=0 w

A: x2+kx+64=0x2-8x+k=0 Take the formula of the discriminant for the real roots, D1,2≥0 where, D=b2-4ac

Q: The false-position method may have difficulty in finding the root of f(x)=x²- 7.4x + 13.69 = 0…

A: According to false position method if roots lies between x1 and x0 Then next approximation will be…

Q: a- Employ the Newton-Raphson method to determine a real root for initial guesses of 4.52 for…

A: Given equation, fx=-1+5.5x-4x2+0.5x3 To find the real root using Newton-Raphson method for initial…

Q: Find a quadratic equation whose product of roots x, and x₂ is X₁ X₂ equal to 4 and satisfying the…

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Q: 10 How many real roots does the quadratic function f (x) = x +6x +9 have? 2. D. cannot be determined

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Q: = (; ). -3 Find the general solutions of X' = AX with A = 1 -2

A: Consider the provided question,

Q: 1. Solve for r in 3+x > 2. 2 - x |

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Q: 17. If f(x) =x -6x +14 and g(x) -x -20x -k, determine the value of k so that there is exactly one…

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Q: 3. How many integer solutions are there to the equa- tion X1 + x2 + x3 = 9, with x; > 0? How many…

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Q: Prove that zero is a root for the equation ax' + bx² +cx+d = 0 if and only if d = 0. What can you…

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Q: n 10x + 11y = n has

A: The equation as, ax+by=S. The smallest positive integer S is expressed as, S=(k+1)*a*b

Q: 8. Find all the roots of f(x) = x' - 4x' +6x² – 4x+5 if 2– i is one root.

A: We will find all the remaining roots as following.

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

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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: Show that the equation x – 15x + c = 0 has at most one root in the interval [-2, 2].

A: Given the function

Q: Select all quadratics which have real zeroes. O f(2) = (z - 4)² – 2 O f(2) O f(x) = 2x + 4r + 4 - 5a…

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Q: 17. If f(x) = x-6x +14 and g(x)-x -20x -k, determine the value of k so that there is exactly one…

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

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Q: 1. Find the solution of the following rational equations and inequalities. x2 – 4 - 1. х — 2 x + 4 -…

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

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

A: Let u and v be the roots of a quadratic equation ax2+bx+c=0. To obtain the equation from the roots,…

Q: Show that the equation x3 - 17x + c = 0 has at most one root in the interval [-2, 2].

A:

Q: 3. Use the Intermediate Value Theorem to show that there is a solution of the equation, ³-4r = 1 in…

A: Explanation of the answer is as follows

Q: 3. Set up the quadratic equation for -7+ 14x = 2x2 - 4. -14+/142 - 4(-2)(-3) a. X = 2(-2) ollo…

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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: Advanced Math Question

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

Q: 17. If f(x) = x -6x +14 and g(x)- x -20x -k, determine the value of k so that there is exactly one…

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Q: Which of the following are the (solutions) of the quadratic belo x2 -9x +8 O(x-1)(x-8) O (x+1)(x+9)…

A: We have to find the root of the quadratic equations

Q: Prove that the equation x- 15x +k = 0 has at most one root in the interval [-2, 2]. Hint: You'll…

A: Dear friend,  if you have any other query about this problem, then please tell me about your query I…

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: (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: Question 5. Find the general solution of t²x" + 3tx' - 3x = t² when t> 0

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Q: If the auxiliary roots of a certain HLDE with constant coefficients are 2, -3, and -3, then the…

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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 :--

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.