Q:If a.ß are roots of ax +2bx +c = 0 and a + 8.ß + 8 be those of b2 - ac в— АС a Ax +2Bx + C = 0, Then prove that A

Q: What is the largest root of the polynomial x? + x – 12? О А. 3 В. 4 О с. 1 O D. 2

A: Using factorisation to find roots

Q: Evaluate: tan -12ß dß. A ß tan-128 – In|1+4ß²| + C B none of the given choices ß tan-12ß+ -In|1+48²|…

A:

Q: 4. Find all the values of the indicated roots a) √4 | b) √√-1-i

A: Step 1:Step 2: Step 3: Step 4:

Q: (2.1) Determine the conjugate of √5+121+√5-12 √5+121-√5-121

A: Replace i with -i to find the conjugate of a complex number.

Q: Find the cofactor of the element a13- -2 -1 0 5 4 2 3 5 O A. 3 О В. 19 ОС. -3 O D. 14 3.

A: Given a square matrix, the cofactor of aij is denoted by Aij=(−1) ^(i+j)M where Mij s the minor of…

Q: ди 82u дх(ду) ду + = u =u

A: The PDE is given by:   ∂2u∂x∂y+∂u∂y=u..................(i) We have to solve the above PDE by using…

Q: If 5 and 7+ √2 are roots of a polynomial with integer coefficients, what must be another root?

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Q: 5. Show that b, is always positive, by establishing the equation (Qn-1,Qn-1) (Qn-2,Qn-2) b,

A: We will apply the properties of inner-product to prove the given statement.

Q: O Let A1, A2, ·.., A5¡be the roots of 6-/51. Show that 51 >d; = 0 i=1

A:

Q: Find the 5th roots of 9. -16/2 + 16vZi

A: =12+32i9De Moivre's theorem;=cosπ3+i sinπ39= eiπ39=ei3π=cos3π + isin3π=-1

Q: 2) × if it was 2+4i and 2=3-1 3+1 2+i 2 prove that x² + 3xy + y² = 6 =

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Q: Use these equations to find az/ax and az/ay for the following. x + y + z = 5xyz дz = əx əz ду =

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Q: b) Let {(-2,–6), (–1,5),(0,4),(1,3)} and {(-2,–18), (-1,–7),(0,–4), (1,–3)} be the point-value…

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Q: Q1) Write the following in scientific notation 1.) 1.234*10 2) -8.765*10402 3.) 1015

A: Given notation can be solved by formulaes

Q: |5πx 106 (4π10-7) [1+ j]J 4

A:

Q: The sun of the roots of 2x +10x-4=0 is

A: x3+a x2+bx+ c = 0 Then sum or roots of this equation is = -a Compare equation 2x3+10x-4 = 0  Then…

Q: Find the cofactor of the element a22- 3 4 4 - 2 -1 1 1 4 1 О А. -8 О в. 8 С. - 1 O D. 1

A:

Q: 3. Determine the 4th roots of -1.25-j2.3.

A: Given,          To determine the roots of the given complex number.

Q: 5. a. Given z, = -7 + 6i(15+2) and z, = -2i(36-0) + 8i , find |z, + z2]. 4 b. Simplify (+ ), and…

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Q: 1) Name the polynomial a) 3x? + 9x - 1 b) 2x* - 9x? - 1

A: a) 3x2+9x-1The above polynomial has a degree 2⇒It is quadratic polynomial

Q: expressions. @-岩。) 3b 9. 2a 2х -3 Зх-2 4. 4x 3 6. 긁-꽃 + 13 7 X-3 2x 3x 8. 5х-20 x2-16 x2- 3x +2 3x-3…

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Q: Factor 10+ 4i into product of primes Z [i], (Hint: Ille= (2)(2)(29)) in %3D

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Q: 10. Use i = (0, 1) and y = (y, 0) to verify that -(iy) = (-i)y. Thus show that the addi- tive…

A: i=0 ,1y=y ,0 verify :   -iy = -iy  To find additive inverse of z=x+iy