- Trending Categories
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
The graphs of $ y=p(x) $ are given in Fig. $ 2.10 $ below, for some polynomials $ p(x) $. Find the number of zeroes of $ p(\bar{x}) $, in each case.
"
Solution:
$( i).\ \because$ The given graph does not touch the $x-axis$ at any point. Thus, number of zeroes is $0$.
$( ii).\ \because$ The graph touches the $x-axis$ at one point. Thus, number of zeroes is $1$.
$( iii).\ \because$ The graph touches the $x-axis$ at three points. Thus, the number of zeroes is $3$.
$( iv).\ \because$ The graph touches the $x-axis$ at two points. Thus, the number of zeroes is $2$.
$( v).\ \because$ The graph touches the $x-axis$ at $4$ points. Thus, the number of zeroes is $4$.
$( vi).\ \because$ The graph touches the $x-axis$ at $3$ points. Thus, the number of zeroes is $3$.
- Related Articles
- The graphs of $y = p(x)$ are given in figure below, for some polynomials $p(x)$. Find the number of zeroes of $p(x)$, in each case.(i)(ii)(iii)(iv)(v)(vi)"
- Find \( p(0), p(1) \) and \( p(2) \) for each of the following polynomials:(i) \( p(y)=y^{2}-y+1 \)(ii) \( p(t)=2+t+2 t^{2}-t^{3} \)(iii) \( p(x)=x^{3} \)(iv) \( p(x)=(x-1)(x+1) \)
- Find the zero of the polynomial in each of the following cases:(i) \( p(x)=x+5 \)(ii) \( p(x)=x-5 \)(iii) \( p(x)=2 x+5 \)(iv) \( p(x)=3 x-2 \)(v) \( p(x)=3 x \)(vi) \( p(x)=a x, a ≠ 0 \)(vii) \( p(x)=c x+d, c ≠ 0, c, d \) are real numbers.
- For which values of \( a \) and \( b \), are the zeroes of \( q(x)=x^{3}+2 x^{2}+a \) also the zeroes of the polynomial \( p(x)=x^{5}-x^{4}-4 x^{3}+3 x^{2}+3 x+b \) ? Which zeroes of \( p(x) \) are not the zeroes of \( q(x) \) ?
- Find the zeros of the polynomial \( x^{2}+x-p(p+1) \).
- Find the value(s) of \( p \) for the following pair of equations:\( -x+p y=1 \) and \( p x-y=1 \),if the pair of equations has no solution.
- Find the value of \( k \), if \( x-1 \) is a factor of \( p(x) \) in each of the following cases:(i) \( p(x)=x^{2}+x+k \)(ii) \( p(x)=2 x^{2}+k x+\sqrt{2} \)(iii) \( p(x)=k x^{2}-\sqrt{2} x+1 \)(iv) \( p(x)=k x^{2}-3 x+k \)
- In the given figure, check if $x+y=p+q$."\n
- Find the zeroes of $P( x)=2x^{2}-x-6$ and verify the relation of zeroes with these coefficients.
- From the choices given below, choose the equation whose graphs are given in Fig. \( 4.6 \) and Fig. 4.7.For Fig. 4. 6(i) \( y=x \)(ii) \( x+y=0 \)(iii) \( y=2 x \)(iv) \( 2+3 y=7 x \)For Fig. \( 4.7 \)(i) \( y=x+2 \)(ii) \( y=x-2 \)(iii) \( y=-x+2 \)(iv) \( x+2 y=6 \)"\n
- Verify whether the following are zeroes of the polynomial, indicated against them.(i) \( p(x)=3 x+1, x=-\frac{1}{3} \)(ii) \( p(x)=5 x-\pi, x=\frac{4}{5} \)(iii) \( p(x)=x^{2}-1, x=1,-1 \)(iv) \( p(x)=(x+1)(x-2), x=-1,2 \)(v) \( p(x)=x^{2}, x=0 \)(vi) \( p(x)=l x+m, x=-\frac{m}{l} \)(vii) \( p(x)=3 x^{2}-1, x=-\frac{1}{\sqrt{3}}, \frac{2}{\sqrt{3}} \)(viii) \( p(x)=2 x+1, x=\frac{1}{2} \)
- Find the value of p for which the quadratic equation $(p + 1)x^2 - 6(p + 1)x + 3(p + 9) = 0, p ≠ -1$ has equal roots. Hence, find the roots of the equation.
- Find the condition that zeroes of polynomial $p( x)=ax^2+bx+c$ are reciprocal of each other.
- Divide the polynomial $p(x)$ by the polynomial $g(x)$ and find the quotient and remainder, in each of the following:$p(x) = x^4 - 5x + 6, g(x) = 2 -x^2$
- Find the zero of the polynomial:$P(x)=x- 5x+6$
Advertisements