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SashulF [63]
4 years ago
10

Graph -x^2+x+6=0 and state the consecutive integers between which roots are located

Mathematics
1 answer:
KengaRu [80]4 years ago
6 0

Answer:

The roots of given quadratic equation lies from \begin{bmatrix}-2 , 3 \end{bmatrix}

Step-by-step explanation:

Given as :

The quadratic equation is x² - x -6 = 0

The quadratic equation is in form of ax² + bx +c = 0

Let x1 and x2 be the roots of equation

Sum of roots

So, x1 + x2 = \frac{-b}{a}  

And products of roots is x1 × x2 = \frac{c}{a}

So, x1 + x2 = \frac{1}{1}  

Or,   x1 + x2 = 1          ......A

And  x1 × x2 = \frac{-6}{1}

Or,  x1 × x2 = - 6

Now, (x1 - x2)² = (x1 + x2)²+ 4×x1×x2

Or,  (x1 - x2)² = (1)²+ 4×6

Or,  (x1 - x2)² = 25

So , x1 - x2 = \sqrt{25} = 5          ......B

Now solve eq A and eq B

Or, (x1 + x2) + (x1 - x2) = 1 +5

Or, 2 x1 = 6

∴   x1 = 3     And     x2 = - 2

Hence The roots of given quadratic equation lies from \begin{bmatrix}-2 , 3 \end{bmatrix}   Answer

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If n and k are positive integers, is n divisible by 6 ? (1) n = k(k + 1)(k – 1) (2) k – 1 is a multiple of 3.
xz_007 [3.2K]

Answer: yes, it is

Step-by-step explanation:

A number is divisible by 6 if it is divisible by 2 and 3 simultaniously.

n = k(k+1)(k-1)

If k-1 is a multiple of 3, n is divisible by 3, so one of the requirements is ok.

Now, if k-1 is a multiple of 3, it can be even or odd.

if k-1 is even, then it is divisible by 2 and as it is divisible by 3 as well, n is divisible by 6

if k-1 is odd, then k and k+1 is even, hence, divisible by 2.

As n = k(k+1)(k-1), n is also divisible by 6.

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Step-by-step explanation:

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PLEA HELP ME WORTH ALOT OF POINTS
Harlamova29_29 [7]
<h2>Answer:</h2>

  • option (c) = -19 + x = -21

<h2>Step by step explanation:</h2>

<u>Question</u> : A number added to -19 is -21

<h3><u>Solution</u> ↓</h3>

First of all to make equation

Equation means LHS = RHS

For eg we take :-

50 - 20 = 10 + 20

30 = 30

Therefore, LHS = RHS

<h3>According to the question :</h3>

  • Which number would we add in -19 to get -21 and we get LHS = RHS

Make an equation

-19 + x = -21

x = -21 + 19

x = -2

Add -2 in the variable of x

Variable means any unknown value we used in maths. For eg :- x,y,z,a,b,c,p,q,r etc.

-19 + (-2) = -21

-19 - 2 = -21

-21 = -21

Therefore, LHS = RHS.

6 0
1 year ago
A=1/2h(a+b) <br> what is h
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Answer:

h = \frac{2 A}{(a + b)}

Step-by-step explanation:

A =  \frac{1}{2} h(a + b) \\  \\2 A =   h(a + b) \\  \\  \frac{2 A}{(a + b)}  = h \\  \\  \huge \red{ \boxed{h = \frac{2 A}{(a + b)} }}

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