Solve the initival value problem: t(t2 +1) 1 r(0) 3r3 V4 r = Hint: Recall that even roots only take in nonnegative numbers and produce nonnegative numbers. Is r(0) positive or negative? Submit answer

Q: Q.1) Evaluate, dr (a) In z dr (b)

A: To find the integral of the given functions.

Q: d) irr(√2+i, 0).

A: One must find the polynomial and check the irreducibility.

Q: If the equation x + ax + bx² + cx + d.= 0 has four real positive roots then (A) ac ≥ 16d (B) b² ≥…

A: We can use Vieta's formulas to relate the coefficients of the quartic equation to its roots. Vieta's…

Q: C (27 – 2r) 139 13

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Q: Show that the roots of px2 + (p - q)x - q = 0 are real for all real values of p and q.

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Q: Which one of the following is a root of √2x1-x+=0? O x = 5 x = 1 O x = 7 x = 3

A: We have to find the roots

Q: For which real numbers x do the following equations hold: (a) Vx + V2x – 1+ Vx – V2x – 1 = V 2а — 1…

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Q: What does Descartes’ Rule of Signs tell you about the real roots of x3 – x2 + 1 = 0 ?

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Q: Determine all real roots of x4 +0.9x³-2.3x²+3.6x-25.2=0

A: We need to find all the real roots of :

Q: 6. If z = a+i is a root of the equation z² – 6z + 10 = 0, find the value of a, if a is a real %3D…

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Q: Q: Solve the following quadratic equati ons by factorization method: 1 1 1 ‚a+b ±0 a+b+x a

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Q: C. (I +3A)−¹ = 2 1 0 -1

A:

Q: Given the quadratic expression p(q) = 2 − r² + 4q − 4 − 7q + 8q² − 10r, identify and state the…

A: Answer:  a=8b=−3c=−2−r2−10rExplanation:Step 1:

Q: Find all the real roots of p(x) = 3x3 – 14x? – 125x + 532 19 given that one of the roots is = 3 19 X…

A: We can solve the problem by doing the multiplication at first.

Q: In the diagram, ABDE is a rectangle, ABCD is equilateral, and AD is parallel to BC. Also, AE = 2x…

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Q: 6. Find the values of k that will make the roots of 3x2- kx +12 = 0 ea

A: Please refer to the image below

Q: 3. Let r be a root of x3 - 5x +7 = 0. In Q[r] express - 1- 7r + 2r2 a) 1+r + r2 | as a quadratic…

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Q: Given x > 0 and y > 0, select the expression that is equivalent to 36x³y8

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Q: . Prove that the equation r – x²+2x +3 = 0 has at least one real root. State the theorems or the…

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Q: Find ‘m’ for which the equation (? − 12)? 2 + 2(? − 12)? + 2 = 0 has equal roots.

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Q: What is the multiplicity of the root r = 2 for the polynomial y = x³ – 3? + 4? O 2 O 4 O 1

A: Given polynomial is, y=x3−3x2+4

Q: For what values of the parameter a does the equation x + 2ax³ + x² + 2ax+1=0 have at least two…

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Q: 12) Consider the polynomial P(x) = 2x + kx? + 7x - 6 %3D a) Find the value of k, such that when P(x)…

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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: 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: 9. (a) Prove that v10 is irrational. (b) Use part (a) to prove that v2 + V5 is irrational.

A: To prove the given statements.

Q: 9 Use Remainder Theorem to find each function value. a) f(x) = 6xª – 5x³ + 8x – 11 - b) Find f(4)…

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Q: The square root property turns (x+3) =16 into x - 3 = 4. O True O False

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Q: Let r₁ and r2 be two different roots of the equation ax² +2bx+c = 0. Without solving the equation,…

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Q: If the sum of the roots of the equation 1/(x + a) + 1/(x + b) 1/c is zero, then prove that the…

A: Given that if the sum of the roots of the equation                   1x+a+1x+b=1c, is zero. To prove…

Q: -1 √₂² (3+2u) du -2

A:

Q: Ben can wash a car in 2 hours while his younger brother James can do it in 3 hours. How long will it…

A: In 1 hour Ben can wash 12 part of car. in 1 hour his younger brother can wash 13 part of car.

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.