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Anton [14]
3 years ago
10

Find the discriminant and determine the nature of the roots to the quadratic equation

Mathematics
1 answer:
Katen [24]3 years ago
3 0
№17
x^{2} +6x-7=0 \\ D=6 ^{2} -4*(-7)=36+28=64=8 ^{2}  \\  \\  x_{1} = \frac{-6+8}{2} =1 \\  \\  x_{2} = \frac{-6-8}{2} =-7
Answer: x₁ = 1
               x₂ = - 7

№18
2 x^{2} -3x+4=3 \\ 2 x^{2} -3x+4-3=0 \\ 2 x^{2} -3x+1=0 \\  \\ D= -3 ^{2} -4*2=9-8=1 \\  \\  x_{1} = \frac{3+1}{2*2} = \frac{4}{4} =1 \\  \\  x_{2} = \frac{3-1}{2*2} = \frac{2}{4} =0.5
Answer: x₁ = 1
               x₂ = 0,5.

№19
2 x^{2} -4x-5=0 \\  D=-4 ^{2} -4*2*(-5)=16+40=56 \\  \\  x_{1}= \frac{4+ \sqrt{56} }{2*2}  = \frac{4}{4} + \sqrt{ \frac{56}{16} } =1+ \sqrt{3.5}  \\  \\  x_{2} = \frac{4- \sqrt{56} }{2*2} = \frac{4}{4} -  \sqrt{ \frac{56}{16} } =1- \sqrt{3.5} 

Answer: x₁ = 1 + √3.5
               x₂ = 1 - √3.5

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Step-by-step explanation:

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(1 point) consider the function f(t)=⎧⎩⎨⎪⎪⎪⎪0,−5,−6,6,t&lt;00≤t&lt;11≤t&lt;7t≥7;f(t)={0,t&lt;0−5,0≤t&lt;1−6,1≤t&lt;76,t≥7; 1. wr
sergij07 [2.7K]
f(t)=\begin{cases}0&\text{for }t

Recall that

u(t)=\begin{cases}0&\text{for }t

Take it one piece at a time. For t\ge0, we can scale u(t) by -5:

-5u(t)=\begin{cases}0&\text{for }t

If we shift the argument by 1 and scale by -5, we have

-5u(t-1)=\begin{cases}0&\text{for }t

so if we subtract this from -5u(t), we'll end up with

-5u(t)+5u(t-1)=\begin{cases}0&\text{for }t

For the next piece, we can add another scaled and shifted step like

-6u(t-1)+6u(t-7)=\begin{cases}0&\text{for }t

so that

-5u(t)+5u(t-1)-6u(t-1)+6u(t-7)=\begin{cases}0&\text{for }t

For the last piece, we add one more term:

6u(t-7)=\begin{cases}0&\text{for }t

and so putting everything together, we get f(t):

f(t)\equiv-5u(t)+5u(t-1)-6u(t-1)+6u(t-7)+6u(t-7)
f(t)\equiv-5u(t)-u(t-1)+12u(t-7)
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