Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$2x^{2}+5mx-3m^{2}=0$ and m is constant, find solution in terms of m $\newline$ A) $\frac{-5m + \sqrt{25m^2 + 24m^2}}{4}$ $\newline$ B) $\frac{-5m - \sqrt{25m^2 + 24m^2}}{4}$ $\newline$ C) $\frac{-5m + \sqrt{49m^2}}{4}$ $\newline$ D) $\frac{-5m - \sqrt{49m^2}}{4}$

View step-by-step help

View step-by-step help

Find derivatives using the quotient rule II

Full solution

Q.

2x^{2}+5mx-3m^{2}=0

and m is constant, find solution in terms of m

\newline

A)

\frac{-5m + \sqrt{25m^2 + 24m^2}}{4}

\newline

B)

\frac{-5m - \sqrt{25m^2 + 24m^2}}{4}

\newline

C)

\frac{-5m + \sqrt{49m^2}}{4}

\newline

D)

\frac{-5m - \sqrt{49m^2}}{4}

Identify coefficients: First, identify the coefficients: $a = 2$ , $b = 5m$ , and $c = -3m^2$ .
Use quadratic formula: Use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
Substitute coefficients: Substitute the coefficients into the formula: $x = \frac{-5m \pm \sqrt{(5m)^2 - 4 \cdot 2 \cdot (-3m^2)}}{2 \cdot 2}$ .
Simplify square root: Simplify inside the square root: $x = \frac{-5m \pm \sqrt{25m^2 + 24m^2}}{4}$ .
Combine like terms: Combine like terms inside the square root: $x = \frac{-5m \pm \sqrt{49m^2}}{4}$ .
Simplify square root: Simplify the square root: $x = \frac{-5m \pm 7m}{4}$ .
Separate solutions: Separate into two solutions: $x = \frac{-5m + 7m}{4}$ and $x = \frac{-5m - 7m}{4}$ .
Simplify each solution: Simplify each solution: $x = \frac{2m}{4} = \frac{m}{2}$ and $x = \frac{-12m}{4} = -3m$ .

More problems from Find derivatives using the quotient rule II

Question

Find the derivative of

f(x)

\newline

f(x) = \cos(x)

\newline

f'(x) =

Posted 5 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \tan(x)

\newline

f'(x) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = e^x

\newline

f'\left(x\right) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \ln(x)

\newline

f'(x) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \tan^{-1}{x}

\newline

f'(x) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = x e^x

\newline

f'\left(x\right) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \frac{e^x}{x}

\newline

f'(x) =

Posted 6 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = e^{(x + 1)}

\newline

f'\left(x\right) =

Posted 5 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \sqrt{x+3}

\newline

f'(x) =

Posted 6 months ago

Question

Find the derivative of

g(x)

\newline

g(x) = \ln(2x)

\newline

g^{\prime}(x) =

Posted 7 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant