Mathematics: Twice a number is added to three times it’s square. if the result is 16, find the number.

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Twice a number is added to three times it’s square.

Ответ:

Ataklty

06.01.2022

Mathematics

ANSWER:

Twice a number is added to three times it’s square. The number is 2, -2.67

SOLUTION:

Let the number be x.

Given, twice a number is added to three times it’s square.

twice a number + three times it’s square

2 $\times$ number + 3 $\times$ numbers square

$2 \times x+3 \times(x)^{2}$

$2 x+3 x^{2}$

Also given that, result is 16. So the above equation is equal to 16

$\begin{array}{l}{2 x+3 x^{2}=16} \\ {3 x^{2}+2 x-16=0}\end{array}$

Let us find roots of above equation using quadratic formula.

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

Here, a = 3, b = 2, c = -16

$\mathrm{x}=\frac{-2 \pm \sqrt{2^{2}-4 \times 3 \times(-16)}}{2 \times 3}$

On simplification we get,

$\begin{aligned} &=\frac{-2 \pm \sqrt{4+12 \times 16}}{6} \\ &=\frac{-2 \pm \sqrt{196}}{6} \\ &=\frac{-2 \pm 14}{6} \\ &=\frac{-2+14}{6}, \frac{-2-14}{6} \\ &=\frac{12}{6}, \frac{-16}{6} \end{aligned}$

x = 2, -2.67

Hence, the value of "x" is either 2 or -2.67

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Twice a number is added to three times it’s square. if the result is 16, find the number.

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