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3 years ago

Find atleast 3 solutions for the following linear equation in two variables:2x + 3y = 4

Mathematics

1 answer:

Anettt [7]3 years ago

7 0

First solution :

Say, x = 0

→ 2x + 3y = 4

→ 2(0) + 3y = 4

→ 0 + 3y = 4

→ 3y = 4

→ y = 4/3

x = 0, y = 4/3

Second solution :

Say, x = 1

→ 2x + 3y = 4

→ 2(1) + 3y = 4

→ 2 + 3y = 4

→ 3y = 4 - 2

→ 3y = 2

→ y = 2/3

x = 1, y = 2/3

Third solution :

Say, x = 2

→ 2x + 3y = 4

→ 2(2) + 3y = 4

→ 4 + 3y = 4

→ 3y = 4 - 4

→ 3y = 0

→ y = 0 ÷ 3

→ y = 0

x = 2, y = 0

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Find all roots: x^3 + 7x^2 + 12x = 0 Show all work and check your answer.

Aliun [14]

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

Solution:

We have been given a cubic polynomial.

$x^{3}+7 x^{2}+12 x=0$

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

$x^{3}+7 x^{2}+12 x=0$

$x\left(x^{2}+7 x+12\right)=0$ ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

$x^{2}+7 x+12=0$

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

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

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

$\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}$

Therefore, the two roots are:

$\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}$

And,

$\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}$

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

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3 years ago

HELP HELP QUICK WILL GET MARKED BRAINLIEST

Harlamova29_29 [7]

Wow the answer is b because you secelted it

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3 years ago

Find atleast 3 solutions for the following linear equation in two variables:2x + 3y = 4​

Find atleast 3 solutions for the following linear equation in two variables:2x + 3y = 4