The distance between 15 and 6 is units.

The difference between the two roots of the equation 3x^2+10x+c=0 is 4 2/3 . Find the solutions for the equation.

andrezito [222]

Answer:

Given the equation: $3x^2+10x+c =0$

A quadratic equation is in the form: $ax^2+bx+c = 0$ where a, b ,c are the coefficient and a≠0 then the solution is given by :

$x_{1,2} = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$ ......[1]

On comparing with given equation we get;

a =3 , b = 10

then, substitute these in equation [1] to solve for c;

$x_{1,2} = \frac{-10\pm \sqrt{10^2-4\cdot 3 \cdot c}}{2 \cdot 3}$

Simplify:

$x_{1,2} = \frac{-10\pm \sqrt{100- 12c}}{6}$

Also, it is given that the difference of two roots of the given equation is $4\frac{2}{3} = \frac{14}{3}$

i.e,

$x_1 -x_2 = \frac{14}{3}$

Here,

$x_1 = \frac{-10 + \sqrt{100- 12c}}{6}$ , ......[2]

$x_2= \frac{-10 - \sqrt{100- 12c}}{6}$ .....[3]

then;

$\frac{-10 + \sqrt{100- 12c}}{6} - (\frac{-10 + \sqrt{100- 12c}}{6}) = \frac{14}{3}$

simplify:

$\frac{2 \sqrt{100- 12c} }{6} = \frac{14}{3}$

or

$\sqrt{100- 12c} = 14$

Squaring both sides we get;

$100-12c = 196$

Subtract 100 from both sides, we get

$100-12c -100= 196-100$

Simplify:

-12c = -96

Divide both sides by -12 we get;

c = 8

Substitute the value of c in equation [2] and [3]; to solve $x_1 , x_2$

$x_1 = \frac{-10 + \sqrt{100- 12\cdot 8}}{6}$

or

$x_1 = \frac{-10 + \sqrt{100- 96}}{6}$ or

$x_1 = \frac{-10 + \sqrt{4}}{6}$

Simplify:

$x_1 = \frac{-4}{3}$

Now, to solve for $x_2$ ;

$x_2 = \frac{-10 - \sqrt{100- 12\cdot 8}}{6}$

or

$x_2 = \frac{-10 - \sqrt{100- 96}}{6}$ or

$x_2 = \frac{-10 - \sqrt{4}}{6}$

Simplify:

$x_2 = -2$

therefore, the solution for the given equation is: $-\frac{4}{3}$ and -2.

3 0

3 years ago

Using a mathematical table evalutate the square root of 0.792

kolezko [41]

Root of 0.792 = 0.89

3 0

2 years ago

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What value of a makes the equation true? a+29=-63 I need help!!

irakobra [83]

Answer:

a = -92

Step-by-step explanation:

Step 1: Subtract 29 from both sides

a + 29 = -63

a + 29 - 29 = -63 - 29

a = -92

Answer: a = -92

7 0

3 years ago

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Kreem has 70 flowers.He gives away some flowers.now he has 2 flowers. how many flowers did Kreem give away.

vova2212 [387]

Answer:

68 flowers

Step-by-step explanation:

70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68. 70-2=68, meaning Kreem has given away 68.

7 0

3 years ago

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Solve this problem 3 Times 7

34kurt

Answer:

3 times 7 is 21

Step-by-step explanation:

4 0

2 years ago

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