Find the roots of the quadratic equation w+w²/3=0

Mathematics

1 answer:

Daniel [21]3 years ago

8 0

I assume that the equation you mean is below:

$\large \boxed{w + \frac{ {w}^{2} }{3} = 0}$

To find roots for this equation, we have to get rid of the denominator. We can do by multiplying both sides by 3.

$\large{w(3) + \frac{ {w}^{2} }{3} (3) = 0(3)} \\ \large{3w + {w}^{2} = 0}$

Factor w-term out (common factor)

$\large{w(3 + w) = 0} \\ \large{w = 0 \: \: \: or \: \: \: 3 + w = 0} \\ \large{w = 0, - 3}$

Answer

The roots of quadratic equation are 0,-3

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The product of a number and -2/3 is -9/10 (20 Points) What is the number?

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Answer:

$\large\boxed{n=\dfrac{27}{20}}$

Step-by-step explanation:

$\text{Let}\ n\ \text{is a number.}\\\\\text{The product of a number and}\ -\dfrac{2}{3}\ \text{is}\ -\dfrac{9}{10}:\\\\-\dfrac{2}{3}\cdot n=-\dfrac{9}{10}\\\\-\dfrac{2n}{3}=-\dfrac{9}{10}\qquad\text{change the signs}\\\\\dfrac{2n}{3}=\dfrac{9}{10}\qquad\text{cross multiply}\\\\(2n)(10)=(3)(9)\\\\20n=27\qquad\text{divide both sides by 20}\\\\\dfrac{20n}{20}=\dfrac{27}{20}\\\\\boxed{n=\dfrac{27}{20}}$