Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

For the following quadratic equation, find the discriminant.

x^(2)-16 x+51=4x-2
Answer:

For the following quadratic equation, find the discriminant. $\newline$ $x^{2}-16 x+51=4 x-2$ $\newline$ Answer:

View step-by-step help

View step-by-step help

Solve exponential equations by rewriting the base

Full solution

Q. For the following quadratic equation, find the discriminant.

\newline

x^{2}-16 x+51=4 x-2

\newline

Answer:

Rephrase the Question: First, let's rephrase the ＂What is the discriminant of the quadratic equation $x^2 - 16x + 51 = 4x - 2$ ?＂
Standard Form Conversion: To find the discriminant, we need to write the quadratic equation in the standard form $ax^2 + bx + c = 0$ . Let's move all terms to one side of the equation to do this. $\newline$ $x^2 - 16x + 51 - (4x - 2) = 0$
Combine Like Terms: Now, let's simplify the equation by combining like terms. $x^2 - 16x + 51 - 4x + 2 = 0$ $x^2 - 20x + 53 = 0$
Identify Coefficients: The standard form of a quadratic equation is $ax^2 + bx + c = 0$ . In our equation, $a = 1$ , $b = -20$ , and $c = 53$ .
Calculate Discriminant Formula: The discriminant of a quadratic equation is given by the formula $D = b^2 - 4ac$ . Let's calculate the discriminant using the values of $a$ , $b$ , and $c$ we found. $\newline$ $D = (-20)^2 - 4(1)(53)$
Perform Calculations: Now, let's perform the calculations. $\newline$ $D = 400 - 4(53)$ $\newline$ $D = 400 - 212$
Find Discriminant Value: Finally, let's subtract $212$ from $400$ to find the value of the discriminant. $\newline$ $D = 188$

More problems from Solve exponential equations by rewriting the base

Question

Solve. Write your answer as an integer or a fraction in simplest form.

\newline

5^x=1

\newline

x=

Posted 2 months ago

Question

Steven opened a savings account and deposited

\$100.00

as principal. The account earns

9\%

interest, compounded annually. What is the balance after

5

\newline

Use the formula

A = P(1 + \frac{r}{n})^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years.

\newline

Round your answer to the nearest cent.

\newline

\$

Posted 2 months ago

Question

Use the following function rule to find

f(1)

\newline

f(x) = 12(7)^x + 8

\newline

f(1) =

Posted 1 month ago

Question

The town of Valley View conducted a census this year, which showed that it has a population of

1,800

people. Based on the census data, it is estimated that the population of Valley View will grow by

12\%

\newline

Write an exponential equation in the form

y = a(b)^x

that can model the town population,

y

x

decades after this census was taken.

\newline

Use whole numbers, decimals, or simplified fractions for the values of

a

b

\newline

y =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = 9^x

\newline

x =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 1 month ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 2 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 1 month ago

Question

g(t) = 3^t

change over the interval from

t = 3

t = 4

\newline

\newline

g(t)

3

\newline

g(t)

3

\newline

g(t)

3\%

\newline

g(t)

200\%

Posted 2 months ago

Question

f(x)

6

over every unit interval in

x

f(0) = 0

\newline

Which could be a function rule for

f(x)

\newline

\newline

f(x) = 6^x

\newline

f(x) = 6x

\newline

f(x) = \frac{1}{6^x}

\newline

f(x) = \frac{x}{6}

Posted 2 months ago