Here we are trying to give the class 9 polynomials extra questions and polynomials class 9 important questions It tests the basic concepts and at the same makes the student comfortable with the questions
Now we know that
$p^3 + q^3 + r^3 -3pqr=(p+q+r)(p^2 + q^2 + r^2 -pq -qr -pr)$
and if p+q+r=0,then
$p^3 + q^3 + r^3=3pqr$
(i) Here $p^2 -q^2 + q^2 -r^2 + r^2 -p^2=0$
$ p -q + q -r + r -p=0$
Therefore
$\frac {(p^2 -q^2)^3 + (q^2 -r^2)^3 + (r^2 -p^2)^3}{(p -q)^3 + (q -r)^3 + (r -p)^3}$
$=\frac {3(p^2-q^2)(q^2 -r^2)(r^2 -p^2)}{3(p-q)(q-r)(r-p)}= (p+q)(q+r)(r+p)$
(ii) Here (x - y)+ (y – z)+ (z - x)=0
Therefore
$(x - y)^3+ (y – z)^3+ (z - x)^3=3(x-y)(y-z)(z-x)$
Question 3
Find the values of a and b if $x^3 -ax^2 -13x +b=0$ has (x-1) and (x+3) as factors Answer
Let f(x) =x^3 -ax^2 -13x +b$
Now f(1)=0 and f(-3)=0
f(1) = 1-a -13+b=0 or b-a=12
f(-3)=9a-b-12=0
On solving both of these
a=3 and b=15
Summary
This Polynomials class 9 extra questions is prepared keeping in mind the latest syllabus of CBSE . This has been designed in a way to improve the academic performance of the students. If you find mistakes , please do provide the feedback on the mail. You can download this test as pdf also as below
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