ints) Check the definiteness of the following quadratic form; Q(x1,x2,x3) = 2xỉ + 3x3 – x + 5x1x3+ x2X3

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: How many inflection points can a: (a) quadratic polynomial have? (b) cubic polynomial have? (c)…

A: fx be a qudratic polynomial .⇒f''x=constant xtherefore a quadratic polynomial never has any…

Q: Show that the square of any positive Integer is of the form 3m or 3m+1 for some integer m

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Q: 29. Select the quadratic polynomial with roots -1 and 4. 22 + 3x – 4 O a3 – 2a? – 7æ – 4 O 4x2 + 8x…

A: It is given that the equation is in quadratic And the two roots of the equations are -1 , 4    This…

Q: Is there a real number whose square is –1? a. Is there a real number x such that _? such that x =…

A: In general, there does not exist any such real number whose square is a negative real number. Hence,…

Q: Which quadratic has zeroes of 5 and 5/2  A) (q + 5)(5q + 2) B) (q - 5)(2q - 5) C) (q - 5)(5q - 2)…

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Q: The number of zeros of the polynomial x? + 2x +3 in Z, is: 1 None 4.

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Q: The quadratic form Q(x) = 3x,² + 7x22 + 4x3? is (a) Positive definite (b) Indefinite (c) Negative…

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Q: Use Gramer Rale Find L3,2 -2x + 33-Z-1 3J-2-1 * + 2y-2- 4 -2x -+2 = -3

A: -2x+3y-z=1x+2y-z=4-2x-y+z=-3 Here, D=-2  3 -1  1  2 -1-2 -1    1,  Dx=  1  3 -1  4  2 -1-3 -1    1,…

Q: The number of zeros of the polynomial x?+ 4x +1 in Zs is:

A: As Z_6 is finite, we check for zeros of polynomial by substituting every  elements of Z_6.

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: The square root property indicates that if x2= k, then x = __________.

A: According to the given information it is required to tell that:The square root property indicates…

Q: 18. Classify the quadratic forms below. a. 9(x1)? – 8x,x2 + 3(x2)? b. -5(x,)? + 4x,x2 - 2(x2)?

A: According to our guideline, we can solve only first question of multiple question. If you want…

Q: The polynomialf(x) = x² + 4x – 2x3 – 1 is a. Nested form b. Linear C. Cubic d. Quadratic

A: The degree of a polynomial is same as the highest power of the variable present in the polynomial.…

Q: Prove that there are no integer solutions to the equation x² = 4y + 3

A: To prove that there are no integer solutions to the equation…

Q: 5 – 4 Given P(x) and that 3i is a zero, write P in factored form (as a 3x x* + 19x* 13x? — 72х — 36,…

A: A function of the form p(x)=anxn+an-1xn-1+⋯+a1x+a0, where, an≠0, a1,a2,...,an∈ℝ and n∈ℕ∪0 is said to…

Q: What is the largest number k for which 2x+3y=20 and 3x+4y=k have the same number if positive integer…

A: Given that, there are two equations following, 2x + 3y = 20…

Q: Factor the following perfect square trinor 49x2 + 14x + 1 O 7(x + 1)2 O (7x - 1) O (x + 7)? (7x +…

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Q: Prove that (x+2) is a factor of 3x'+8x+x-6 and find the other factor.

A: we have to find factor of the polinomial

Q: Determine the enlue of K for which the systm hab no Solutions X+y * +२7 -रेच 2 3 +52=0 3x + 9y…

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Q: Do not use a calculator in this question. Find the positive value of x for which (4 + V5)x² + (2 –…

A: 3 Given equation is 4+5x2+2−5x−1=0. We have to find the positive value of x. The solution of the…

Q: Based on the Fundamental Theorem of Algebra, how many zeros does the polynomial z - 3z-5z +15r? -…

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Q: Show if z = 2 + 4i satisfies z? – 4z + 20 = 0

A: To show that a value or number satisfies an equation, we substitute the value in the equation and…

Q: If s is neative, its square must be

A: Given s is negative  s < 0

Q: The form of decomposing a single irreducible quadratic factor in agiven intecral is /(2ax +b)A+B…

A: We have to identify the given statement as true or false.

Q: A farmer’s rectangular field has an area that can be expressed as thetrinomial x2 + 2x + 1. In terms…

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Q: ! and A quadratic polynomial y = 4x? + 7x – 3 has roots pand q. Find a quadratic g(x) = x2 + ax + B…

A: To find out the quadratic equation.

Q: 11/15 Correct P(x) = 4x4 – 20x³ + 15x² + 5x – 4 e quadratic formula, if necessary, to identify the…

A: In this question we will use basic of polynomial function i.e finding zeros of the polynomial. We…

Q: (c) Determine the definiteness of the quadratic form q(x) = xỉ +2/6x,6x2 + 2x3

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Q: (c) Determine the definiteness of the quadratic form q(x) = xỉ + 2V6x1x2 + 2x3 %3D

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: The solutions of the quadratic equation x(4x – 3) + 3 = 0 are - O None of these O 3±iv57 8. O…

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Q: Use the Cayley - Hamilton theorem to calculate 3 -2 -1 A-1 and A4 if A = 3 4 -2

A:

Q: The area of a rectangular patio is 3x^2+17x+20ft^2. Which of the following could be dimensions of…

A: Given area of rectangular patio,  (3x2 + 17x +20)ft2 To find the dimensions of the patio.

Q: (c) Determine the definiteness of the quadratic form q(x) = xỉ + 2/6x16x2 + 2x3

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Q: By using this 3B=5 St Xj <B Vj EN Poove

A: See the attachment

Q: HwO Use Gramer Rale to Find 4,2 -2x + 3-Z = 1 X + 2y-2- 4 -2x -y +2 = -3

A: As per guideline we have to solve only one

Q: 29. Select the quadratic polynomial with roots –1 and 4. x2 + 3x – 4 x3 – 2x2 – 7x – 4 4x² + 8x + 4…

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Q: Evaluate the integral 1 xp- 9x² + 6x – 8 by first completing the square and using the substitution u…

A: The given integral is: ∫19x2+6x-8dx To evaluate this integral, first, make the square by adding and…

Q: The form of decomposing a single irreducible quadratic factor in agiven inteeral is / (2ax+b)A+B dx.…

A: To write that it is true or false.

Q: 3) a,²+3+3<-2223

A: Quadratic form is x12+3x22+3x32-2x2x3 The matrix of the above quadratic form is  A=10003-10-13

Q: Use complex analysis to prove the formula 2n n 7 7n V 3 n=0

A: It is given that

Q: The product rule for square roots states that if a and b are nonnegative, then √ab =______.

A:

Q: b) The polynomi al PGX) =x"+mx²+42x²+nx+65, where m and n are real, has zeros 3+2i and 1-i. :) Write…

A: Kindly note that there is misprint in question which is mentioned at the end of solution.

Q: Use the given zero to write P(x) as a product of linear and irreducible quadratic factors. P(x) =x…

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Q: Determine the definiteness of the quadratic form q(x) = xỉ + 2V6x,X2 + 2x3

A:

Q: what is the remaining real zeros for P(x)= x cubed plus x squared minus four x minus 4

A: Given:P(x) = x3 + x2 - 4x -4

Q: (i) q(x) = 3x2 + 2xy +5yz + 7y2 – 2z2 %3D -

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Q: (c) Determine the definiteness of the quadratic form q(x) = x} + 2V6x,Xz + 2x3

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Q: Which polynomial has 3i, -3i, and 3 (with multiplicity 2) as its roots? A x3 - 3x? + 9x + 27 B x* –…

A: Options  x3 - 3x2 +9x + 27  x4 – 6x3 + 54x - 81  x4 - 6x3 + 18x2 - 54x + 81  x4 - 6x3 + 12x2 - 18x…