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The difference between the roots of the equation 3x2+bx+10=0 is equal to 4 1 3 . find<br> b.

inna [77]

Given that the difference between the roots of the equation $3x^2+bx+10=0$ is $4 \frac{1}{3} = \frac{13}{3}$ .

Recall that the sum of roots of a quadratic equation is given by $- \frac{b}{a}$ .

Let the two roots of the equation be $\alpha$ and $\alpha + \frac{13}{3}$ , then

$\alpha + \alpha + \frac{13}{3} =2 \alpha + \frac{13}{3} =- \frac{b}{a} =- \frac{b}{3} \\ \\ i.e.\ \ 2 \alpha + \frac{13}{3}=- \frac{b}{3}$ . . . (1)

Also recall that the product of the two roots of a quadratic equation is given by $\frac{c}{a}$ , thus:

$\alpha \left( \alpha + \frac{13}{3} \right)= \alpha ^2+ \frac{13}{3} \alpha = \frac{c}{a} = \frac{10}{3} \\ \\ i.e.\ \ \alpha ^2+ \frac{13}{3} \alpha=\frac{10}{3}$ . . . (2)

From (1), we have:

$2 \alpha =- \frac{b}{3} - \frac{13}{3} \\ \\ \Rightarrow \alpha =- \frac{b}{6} - \frac{13}{6}$

Substituting for alpha into (2), gives:

$\left(- \frac{b}{6} - \frac{13}{6}\right)^2+ \frac{13}{3} \left(- \frac{b}{6} - \frac{13}{6}\right)= \frac{10}{3} \\ \\ \Rightarrow \frac{b^2}{36} + \frac{13b}{18} + \frac{169}{36} - \frac{13b}{18} - \frac{169}{18} = \frac{10}{3} \\ \\ \Rightarrow \frac{b^2}{36} - \frac{289}{36} =0 \\ \\ \Rightarrow \frac{b^2}{36} = \frac{289}{36} \\ \\ \Rightarrow b^2=289 \\ \\ \Rightarrow b=\pm\sqrt{289}=\pm17$

5 0

3 years ago

the length of a rectangle is 6 inches less than 4 times the width of the rectangle , write an expression to find the perimeter o

Aleks04 [339]

Answer:

x + (4x-6) • 2

Step-by-step explanation:

First, let's start by calling the width of the rectangle x

Because the length is 4 times the width minus 6, the equation for length will be 4x-6

The width and length together will be x + (4x-6)

You then have to times it by 2 to find the whole perimiter.

4 0

3 years ago

Adam buys a cubical box to mail a package. The volume of this box is 216 cubic inches. What is the length of one side

BartSMP [9]

Let V=216
formula for volume=a^3
V=a^3
216=a^3
now by taking cubert on both sides
cuberoot(216)=cuberoot(a^3)
a=6
so the length of one side will be 6m

7 0

3 years ago

Question 15(Multiple Choice Worth 1 points) (06.04 MC) The expression to find the perimeter of a rectangle is 2(length + width).

vodomira [7]

Answer: 1 2/3

Step-by-step explanation:

The expression to find the perimeter of a rectangle is 2(length + width)

Length = 1/3

Width = 1/2

Perimeter = 2( 1/3 + 1/2)

Lowest common factor = 6

Perimeter = 2 [ (2 + 3) / 6]

Perimeter = 2 [ 5/6]

Perimeter = 10/6

Perimeter = 1 4/6 = 1 2/3

5 0

3 years ago

Plsss help ill give brainly

maw [93]

Answer:

7,7

Step-by-step explanation:

A vertex should be connected, so 7 as the x makes the most sense

3 0

2 years ago

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