Answer

Verified

399.3k+ views

**Hint:**\[x\] and \[y\] intercepts for the given expression can be found by keeping one of the variables as zero. That is, to find the x intercept, the point at which the equation intersects the x-axis, we will have to keep \[y=0\] and to find the y intercept, the point at which the equation intersects the y-axis, we will have to keep the \[x=0\].

**Complete step-by-step solution:**

x- intercept refers to the point in the graph of a given equation which intersects the x-axis. At that point, y-coordinate will be zero. This information is important to find the x-intercept else we will have to draw the graph of the given equation.

Similarly, y- intercept refers to the point in the graph of a given equation which intersects the y-axis. At that point, x coordinate will be zero. This information is important to find the y-intercept else we will have to draw the graph of the given equation. We will verify our answer with the help of a graph at the end.

According to the given question, we are to find the \[x\] and \[y\] intercepts for \[y=2{{x}^{3}}+3x-5\],

Let’s start with finding x-intercept,

We will take \[y=0\]

So the equation gets the form,

\[2{{x}^{3}}+3x-5=0\]

Now solving the equation for the value of \[x\], since the degree of the polynomial is 3, we will get three values of \[x\].

\[\Rightarrow 2{{x}^{3}}+3x=5\]

Taking \[x\] common, we get

\[\Rightarrow x(2{{x}^{2}}+3)=5\]

We have \[x=5\] and \[2{{x}^{2}}+3=5\]

So, one value of \[x=5\], since it does not satisfy the equation it is removed, solving other part,

\[2{{x}^{2}}+3=5\]

\[\Rightarrow 2{{x}^{2}}=2\]

\[\Rightarrow {{x}^{2}}=1\]

\[x=\pm 1\]

Since, \[x=-1\]does not satisfy the equation it is removed as well.

Now, we only have \[x=1\]

So, we get the value of x-intercept in the equation: \[(1,0)\]

Now, let’s find the y-intercept,

We will take \[x=0\], we get the equation as

\[y=2(0)+3(0)-5\]

\[y=-5\]

So, the y-intercept is \[(0,-5)\].

Therefore, the \[x\] and \[y\] intercepts for \[y=2{{x}^{3}}+3x-5\] are:

x-intercept in the equation is \[(1,0)\]

y-intercept is \[(0,-5)\]

**Note:**\[x\] and \[y\] intercept are found by taking \[y=0\] and \[x=0\] respectively. It should be kept in mind while doing the calculation and not interpreted the other way round. Also while substituting the values of \[x\] and \[y\], it should be calculated carefully else will result in a wrong answer.

Recently Updated Pages

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Advantages and disadvantages of science

Trending doubts

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

How do you graph the function fx 4x class 9 maths CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Give 10 examples for herbs , shrubs , climbers , creepers

Change the following sentences into negative and interrogative class 10 english CBSE