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Amiraneli [1.4K]
3 years ago
13

Prove that if one solution for a quadratic equation of theform x2 + bx + c = 0 is rational (where b and c are rational),then the

other solution is also rational. (Use the factthat if the solutions of the equation are r and s, thenx2 + bx + c = (x − r )(x − s).)
Mathematics
1 answer:
Elenna [48]3 years ago
7 0

Answer:

The other solution of the given equation x² + bx + c = 0   is also rational number.

Step-by-step explanation:

Here, given: ax² + bx + c = 0 is a quadratic equation

Also, one solution  (r)  of equation is RATIONAL.

To show: The other solution (s)  is also RATIONAL

Now, here: as x² + bx + c = 0

Since r and s are the two given solutions, the given equation can be factorized as:

x² + bx + c =  (x -r) (x - s)

Simplifying LHS, we get:

(x -r) (x - s) = x x - r (x) - s (x) +  (r)(s)

                 =  x² + x(-r - s) +  rs

or, x² + bx + c = x² + x(-r - s) +  rs

Comparing the related terms, we get:

b =  (-r - s)    

⇒  b +  s = - r

or, s  = -r - b

Now, given : r = Rational  and the negative of a rational is also rational.

⇒  -r is also rational

Also, difference of two rational number is also rational.

⇒ -r - b is also rational

⇒ s is a RATIONAL NUMBER

Hence, the other solution of the given equation x² + bx + c = 0   is also rational number.

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Answer:

44h

Step-by-step explanation:

Auto repair shop Charge - $36

Replaced Parts - $8

Number of Hours - h

Formula to find the total cost

(Auto Repair Shop Charge + Replaced Parts) x Number of Hours

= (36 + 8) x h

= 44 x h

= 44h

3 0
2 years ago
What is the product of 2x- 1 and x+4
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(2x - 1) \times (x + 4)
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3 years ago
Can anyone help with this?
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Answer:

46

Step-by-step explanation:

The complete square starting with x^2+14x would be x^2+14x+49, since the square would be (x+7)^2. To make this square perfect, then, you would need to add 46 to make 49 with the 3. Hope this helps!

6 0
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A basketball player attempts 18 baskets in a game. He makes 8 of the attempted baskets. Which ratio describes the number of bask
EleoNora [17]

Answer:

4:9

Step-by-step explanation:

8:18 in simplest form is 4:9

7 0
2 years ago
I need help , if yk the answer help fr!!!
Feliz [49]

Answer:

The measure of the angle JKG is:

m∠JKG = 56°

Step-by-step explanation:

<u>Given</u>

m∠JKG = 76-2x

m∠FHK = 6x-4

J is a midpoint of the segment FG and K is a midpoint of the segment GH.

<u>To determine</u>

m∠JKG = ?

Given that J is a midpoint of the segment FG and K is a midpoint of the segment GH. Thus, making two similar triangles, ΔJGK and ΔFGH

We know that two triangles are similar if the only difference is size. So, the angles remain the same.

so m∠JKG and m∠FHK are equal.

i.e.

m∠JKG = m∠FHK

substitute m∠JKG = 76-2x and m∠FHK = 6x-4

76-2x = 6x-4

6x+2x = 76 + 4

8x = 80

divide both sides by 8

8x/8 = 80/8

x = 10

Therefore, the value of x = 10

As

m∠JKG = 76-2x

substitute x = 10

m∠JKG = 76 - 2(10)

             = 76 - 20

             = 56°

Therefore, measure of the angle JKG is:

m∠JKG = 56°

4 0
2 years ago
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