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3 years ago

Use the discriminant to determine the nature of the roots of the following equation.

Mathematics

1 answer:

kvv77 [185]3 years ago

4 0

Discussion

The discriminate is b^2 - 4*a*c

The general equation for a quadratic is ax^2 + bx + c

In this equation's case

a = 1

b= -5

c = - 3

Solve

(-5)^2 - 4*(1)*(-3)

25 - (-12)

25 + 12

Note

Since the discriminate is > 0, the roots are real and different. The roots do exist and there are 2 of them.

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Find the solutions to the equation below 30x^2-28x+6 =0

Naddik [55]

For this case, we have the following equation of the second degree:

$30x ^ 2-28x + 6 = 0$

If we divide between 2 on both sides of the equation, we will have:

$15x ^ 2-14x + 3 = 0$

Where:

$a = 15\\b = -14\\c = 3$

The solutions will come from:

$x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}$

Substituting:

$x = \frac {- (- 14) \pm \sqrt {(- 14) ^ 2-4 (15) (3)}} {2 (15)}\\x = \frac {14 \pm \sqrt {196-180}} {30}\\x = \frac {14 \pm \sqrt {16}} {30}\\x = \frac {14 \pm4} {30}$

So, we have:

$x_ {1} = \frac{14 + 4} {30} = \frac {18} {30} = \frac {18} {30} = \frac {3} {5}\\x_ {2} = \frac {14-4} {30} = \frac {10} {30} = \frac {1} {3}\\$

Answer:

$x_ {1} = \frac {3} {5}\\x_ {2} = \frac {1} {3}$

Option A

Option E

6 0

3 years ago

Read 2 more answers

Nathan usually drinks 32 ounces of water per day. He read that he should drink 56 ounces of water per

MariettaO [177]

Answer:

Step-by-step explanation: you have to find the amount of change then determine the percent of increase and round it to the nearest percent

32 -56=24 then round to the nearest number you get 20

7 0

3 years ago

Find the missing value. (√24-√k)(√24+√k)=5

Anna [14]

Answer:

k = 19

Step-by-step explanation:

Identity

(a + b)(a - b) = a² - b²

Simplifying the LHS (Left Hand Side)

(√24-√k)(√24+√k)
(√24)² - (√k)²
24 - k

Equating to the RHS

24 - k = 5
k = 24 - 5
k = 19

4 0

3 years ago

Read 2 more answers

A stack of 20 coins contains only nickels and

Galina-37 [17]

Answer:

16 quarters and 4 nickels

4×25=1.00 × 4 = 4.00 4×4=16-quarters

20-16=4-nickels

Step-by-step explanation:

Hope this helps!

7 0

3 years ago

The base of a triangle is 7 inches more than 4 times the height. If the area of the triangle is 93 square inches, find the base

Galina-37 [17]

Answer:

Step-by-step explanation:

Let the height = h

Let the base = 4h + 7

Area of a triangle = 1/2 * b * h

Area = 93 square inches

1/2 * (4h + 7)* h = 93 Multiply both sides by 2

(4h + 7) * h = 93*2

(4h + 7)*h = 186 Remove the brackets

4h^2 + 7h = 186 Subtract 186 from both sides.

4h^2 + 7h - 186 = 0

Use the quadratic formula to solve

a = 4

b = 7

c = - 186

x1 = (-7 + sqrt(7^2 - 4*4*(-186) ) /2*4

x1 = (-7 + sqrt(49 - 16*(-186)) / 8

x1 = (-7 + sqrt(49 + 2976)) / 8

x1 = (-7 + sqrt(3025)) / 8

x1 = (-7 +55 ) / 8

x1 = (48)/8

x1 = 6

There is another root, but it has to be minus and therefore cannot be used as a length. x2 = - 7.75

h = 6

b = 4*6 + 7 = 31

Check

Area = 1/2 * b * h

Area = 1/2 * 31 * 6

Area = 1/2 *186

Area = 93 which is what we were given so the answer is correct.

4 0

2 years ago