2.3 Theorem. Let p(x) be an irreducible polynomial in F[x). Then there exists an extension E of F in which p(x) has a root.

Q: Solve     3tan2 x − 1 = 0.

A:

Q: Psr Solve for x Ix+s\=-4

A: We have to Solve for x.

Q: Solve for x: 3* = 23

A: Given, 3x = 23  We have to solve for x.

Q: Solve x+ 3 <5.

A:

Q: Solve (5 + 2/6 )* -3+ (5 – 2/6)**-3 = 10

A:

Q: 15x* – 30Ľ x +7L = 0 ² %3D

A:

Q: What value of x will make the length of the box three times as big as the width?

A: see below the answer and explanation

Q: 2a. Find an interval containing a root of x - 3X = %3D

A: Given equation is x - 3-x = 0 Let,  f(x) =  x - 3-x       clearly f is a continuous function of x.…

Q: Solve for x 10 x-2 2.

A: To find the value of x

Q: 3x+1 4. < 2 X-1

A: Solving for interval that satisfies the given inequality.

Q: yt + x* = F g?

A: Given that: y4+x4=x5y7 Now, take the all "y" terms on one side, we get: y7x5-y4=x4 Now take the…

Q: e. 5 = logx 25 f. 3.5 = log36 X

A:

Q: 9(10*-2) = 34. %3D

A:

Q: 2) Solve for x: 3* = 27

A: Solution ) 3x = 1/27              3x = 1 / 33                    3x  = 3-3  (We know am = an  so m=…

Q: =8 + = 6 13 8 Time 2 hours = 00 +

A:

Q: 2a. Find an interval containing a root of x - 3X =

A:

Q: 4 mi 3 mi

A:

Q: 32 9 24

A: Use Thales theorem  Use tales theorem

Q: Solve for X. X = -8 X = I.

A:

Q: 500 (2) 43 = 100

A:

Q: If 2* = 8*-1, solve for x.

A:

Q: Solve completedy: he ak y ayax

A: Partial differential equation

Q: solve for x 8/x+1 - 3/2= 6/3x+3

A: Given,

Q: 2. Show two ways of solving the following: 3*+2 – 3* = 216

A:

Q: Solve for x. 9*-4-27

A:

Q: 2 = 1 +| Month:

A: To solve 1+1

Q: Find the exact value of E 75 2k²+2 uk=1 3

A:

Q: Solve for x a. 375³x+5 = 25*-7 b. 7²* = 2(7¹) +3

A:

Q: x² +1/x² = 34 , find the value of x⁴ + 1/x

A: Square the given expression