Answer
385.5k+ 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.
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 \[(0,-5)\].
![seo images](https://www.vedantu.com/question-sets/7ead05f8-9acb-4a8a-bd23-ff28f08b53c65875563569647442457.png)
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
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)