1-x 2 3 If 0 x 0 = 0, then its roots are: (a) 1 only (b) 0,1 (c) 0 only (d) -1,0,1 Select the correct response: a b

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: If y = C1 + C2x +e2*(C3cosx + C4sinx), then the roots are

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Q: Find a quadratic equation whose product of roots x₁ and X2 equal to 4 and satisfying the relation X₁…

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Q: Find all the zeros given that z 2 and z=-7 are zeros: j (z) = 4x + 19z - 64z2 -I+ 42 %3D %3D %3D O x…

A: Answer

Q: D 20. Marco wants to show that x³-y - (x-y)x² +xy +y is true for all values of x and y. Marco makes…

A: The given identity is  x3-y3= (x-y)(x2+xy+y2)

Q: Note: m=2 n=8 Answer the following questions a. Simplify the following polynomial and answer the…

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Q: (~-()' 15 3 20

A: a) Evaluate  (i20-(1i)15)3 =(i20-1i15)3 ={(i2)10-1i(i2)7}3 we know that i2=-1={(-1)10-1i(-1)7}3…

Q: How many roots are there for the polynomial that factors into f(x) = (x² – 1)(x + 2)(æ – 1)2? 3.

A: no of roots = ?

Q: 9. Graph Identify end behavior, x and y intercept , optional point and graph F(x) = x ( x-1) ( x + 3…

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Q: 5 Calculate the roots of the following polynomial equations: (a) x³ – 6x² + 11x – 6 = 0 given x = 1…

A: Topic = Polynomials

Q: Multiply and simplify. X- 1 x2 - 1 x2 +2x +1 X +1

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Q: Use the value of the discriminant, b² - 4ac, to determine the number and type of roots for x²-3x+7=0…

A: We have to use the value of the discriminant, b²-4ac, to determine the number and type of roots for…

Q: Vx² + 4x – 5 dr. A secant substitution Evaluate x + 2

A: Consider the following definite integral: ∫14x2+4x-5x+2dx=∫14x2+4x+4-9x+2dx=∫14x+22-9x+2dx…

Q: If p(q=r) prove that x +q{r-p}x+p-q) = 0 has equal roots, ther 211 q = р

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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: The polynomial y = x³ + æ³ – a? – 1 factors into (x? + 1)(x³ – 1). What is the multiplicity of the…

A: Polynomial y = x5+x3-x2-1Factored form: x2+1x3-1Equate x3-1 = 0                +1     +1x3 = 1Taking…

Q: '-7r + 19r- 13 and write it as the product of three 2. (3.4) Factor the polynomial P(r)-r linear…

A: Substitute x=1 in the given equation Then P(x)=0 So (x-1) is a factor of P(x)

Q: Which of the following are the solutions to the polynomial equation x - 13x +36 0? O a. x = 0, 4, 9…

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Q: Prove that 3x3+ 5x - 11 has a root between x=1 and x=2. Thanks!

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Q: Which of the following expressions has the greatest common monomial factor of 4x y? O 17x3y + 8y3-…

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Q: 6. If f(x)= 9x²+3x -10, determine f(-1) (2a5b)³ 7. Simplify the following using only positive…

A: .

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: Given the polynomial y = 10x³ – 27x? + 15x – 2, a. list all possible numerators for rational roots…

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Q: (w- 2)² =O

A: Topic:- algebra

Q: Find the roots of the function h(z) 4 %3D Z-5 Z-8 27

A: We have to find the roots of the function  h(z) = zz-5-4z-8.

Q: (a + 2b-3c) (ab+c).

A: let  I=(a+2b-3c)(a-b+c)

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: Find the roots of the polynomial: f (x) = 2(x – 5)³ + 16.

A: Given f(x)=2x-53+16

Q: 3 The degree of polynomial = The coefficient of x4 i. ii. iii. Constant term =

A: This is a problem of Number Theory.

Q: 2x2 +x + 1 dx (x+1)(x2 + 1)

A:

Q: 5. Solve xdx + ydy = xdy – ydx %3D |

A: Introduction :