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Vladimir79 [104]
3 years ago
5

How do you illustratequadratic equationin one variable?​

Mathematics
1 answer:
soldi70 [24.7K]3 years ago
4 0

Step-by-step explanation:

Quadratic Equation

Quadratic equation is in the form

ax2+bx+c=0

Where

a, b, & c = real-number constants

a & b = numerical coefficient or simply coefficients

a = coefficient of x2

b = coefficient of x

c = constant term or simply constant

a cannot be equal to zero while either b or c can be zero

Examples of Quadratic Equation

Some quadratic equation may not look like the one above. The general appearance of quadratic equation is a second degree curve so that the degree power of one variable is twice of another variable. Below are examples of equations that can be considered as quadratic.

1. 3x2+2x−8=0

2. x2−9=0

3. 2x2+5x=0

4. sin2θ−2sinθ−1=0

5. x−5x−−√+6=0

6. 10x1/3+x1/6−2=0

7. 2lnx−−−√−5lnx−−−√4−7=0

For us to see that the above examples can be treated as quadratic equation, we take example no. 6 above, 10x1/3 + x1/6 - 2 = 0. Let x1/6 = z, thus, x1/3 = z2. The equation can now be written in the form 10z2 + z - 2 = 0, which shows clearly to be quadratic equation.

Roots of a Quadratic Equation

The equation ax2 + bx + c = 0 can be factored into the form

(x−x1)(x−x2)=0

Where x1 and x2 are the roots of ax2 + bx + c = 0.

Quadratic Formula

For the quadratic equation ax2 + bx + c = 0,

x=−b±b2−4ac−−−−−−−√2a

See the derivation of quadratic formula here.

The quantity b2 - 4ac inside the radical is called discriminat.

• If b2 - 4ac = 0, the roots are real and equal.

• If b2 - 4ac > 0, the roots are real and unequal.

• If b2 - 4ac < 0, the roots are imaginary.

Sum and Product of Roots

If the roots of the quadratic equation ax2 + bx + c

= 0 are x1 and x2, then

Sum of roots

x1+x2=−ba

Product of roots

x1x2=ca

You may see the derivation of formulas for sum and product of roots here.

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3 years ago
I really need help rn T_T plz help me out!
pshichka [43]

Answers:

  • The lengths of sides PQ and RS are <u>   13   </u>
  • The lengths of sides QR and SP are <u>   </u><u>20  </u>

This is a 13 by 20 rectangle.

============================================================

Explanation:

Refer to the drawing below.

Let x be the length of side SP. Since we're dealing with a rectangle, the opposite side is the same length. Side QR is also x units long.

We're told that RS = SP - 7 which is the same as saying RS = x-7

We also know that PQ = x-7 as well because PQ is opposite side RS.

In short, we have these four sides in terms of x

  • PQ = x-7
  • QR = x
  • RS = x-7
  • SP = x

as shown in the drawing. The four sides add up to the perimeter of 66.

PQ+QR+RS+SP = perimeter

PQ+QR+RS+SP = 66

(x-7)+x+(x-7)+x = 66

4x-14 = 66

4x = 66+14

4x = 80

x = 80/4

x = 20

Use this x value to find the unknown side lengths.

  • PQ = x-7 = 20-7 = 13
  • QR = x = 20
  • RS = x-7 = 20-7 = 13
  • SP = x = 20

In short, this is a 13 by 20 rectangle.

-----------------

Check:

perimeter = side1+side2+side3+side4

perimeter = PQ+QR+RS+SP

perimeter = 13+20+13+20

perimeter = 33+33

perimeter = 66

The answer is confirmed.

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Answer:

The constant of proportionality is 2.

Step-by-step explanation:

In an equation for which we are looking for the constant of proportionality, we use the base form below.

y = kx

In which k is the constant of proportionality. If we use the equation given

y = 2x

We can see k = 2

8 0
3 years ago
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