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2 years ago

Write the quadratic equation whose roots are 3 and 1, and whose leading coefficient is 1

Mathematics

1 answer:

Serhud [2]2 years ago

6 0

Answer:

x² - 4x + 3 = 0

Step-by-step explanation:

given roots x = a and x = b then the corresponding factors are

(x - a) and (x - b)

the equation is then the product of these factors , that is

(x - a)(x - b) = 0

given

roots x = 3 and x = 1 , then factors are (x - 3) and (x - 1) , then

(x - 3)(x - 1) = 0 ← expand factors using FOIL

x² - 4x + 3 = 0

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3 years ago

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3 years ago

A) Find a particular solution to y" + 2y = e^3 + x^3. b) Find the general solution.

Reptile [31]

Answer:

a.P.I= $\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)$

b.G.S= $C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x}$

Step-by-step explanation:

We are given that a linear differential equation

$y''+2y=e^{3x}+x^3$

We have to find the particular solution

P.I= $\frac{e^{3x}}{D^2+2}+\frac{x^3}{D^2+2}$

P.I= $\frac{e^{3x}}{3^2+2}+\frac{1}{2} x^3(1+\frac{D^2}{2})^{-2}$

P.I= $\frac{e^{3x}}{11}+\frac{1-2\frac{D^2}{4}+3\frac{D^4}{16}+...}{2}x^3$

P.I= $\frac{e^{3x}}{11}+\frac{x^3-2\frac{\cdot3\cdot 2x}{4}}{2}+0}$ (higher order terms can be neglected

P.I= $\frac{e^{3x}}{11}+\frac{1}{2}(x^3-3x)$

b.Characteristics equation

$D^2+2=0$

$D=\pm\sqrt2 i$

C.F= $C_1cos \sqrt2x+C_2 sin\sqrt2 x$

G.S=C.F+P.I

G.S= $C_1Cos \sqrt2 x+C_2 Sin\sqrt2 x+\frac{1}{11}e^{3x}+\frac{1}{2}(x^3-3x)$

3 0

3 years ago

The square root of 68 is between what two consecutive whole numbers

Pavel [41]

The two consecutive numbers are 8 and 9.

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3 years ago

The dividend is a factor of 60. The divisor is a factor of 18. The quotient is a multiple of 3. Use the numbers to find one poss

Anna007 [38]

Answer:

The dividend is 360, divisor is 6 and quotient is 60.

Step-by-step explanation:

Factors of 3= 3*1

Factors of 18= 3*2*3

Factors of 60= 3*2*2*5

Taking LCM= 3*2*2*2*3*5= 360

60 is a factor of 360

The dividend is 360

If 360 is divided by 6 we get 60 which is a multiple of 3

and 6 is a factor of 18.

Therefore the dividend is 360 divisor is 6 and quotient is 60.

6 0

3 years ago