Given below are the Class 10 Maths Worksheet for Polynomials
a. cubic polynomials problems
b. quadratic polynomials Problems
c. Word Problems

Question 1 Verify the 1/2 ,1, -2 are zeroes of cubic polynomial 2x^{3} + x2 -5 + 2. Also verify the relationship between the zeroes and their coefficients. Question 2 p and q are zeroes of the quadratic polynomial x^{2} – (k + 6)x + 2(2k – 1). Find the value of k if 2(p+q) =pq Solution

for f(x)=x^{2} – (k + 6)x + 2(2k – 1)
We get,
p+q = k+6
pq = 2(2k-1)
Now
2(p+q) =pq
Therefore,
2(k+6) = 2(2k-1)
or k+6=2k-1
or k=7

Question 3 m, n are zeroes of ax^{2 }– 5x + c. Find the value of a and c if m + n = m. n = 10. Solution

for f(x)=ax^{2 }– 5x + c
we get
m+n=5/a
mn=c/a
Given m + n = m. n = 10
Therefore,
5/a=10
a=1/2

c/a=10
or c=5

Question 4 If a and b are zeroes of the x^{2} + 7x + 7, find the value of a^{-1} + b^{-1 }-2ab Solution

for f(x)=x^{2} + 7x + 7
we get
a+b=-7
ab=7
Now
a^{-1} + b^{-1 }-2ab
= (a+b-2(ab)^{2})/ab
= -7-98/7=-15

Question 5 Find remainder when x^{3} – ax^{2} + 6 – a is divided by (x – a). Solution

Given p(x) =x^{3} – ax^{2} + 6 – a
By remainder theorem
p(a) = 6-a

Question 6 If p and q are zeroes of f(x) = x^{2 }– 5x + k, such that p -q = 1, find the value of k. Solution

for f(x)=x^{2 }– 5x + k
we get
p+q= 5
pq=k
Now
p -q = 1
(p -q)^{2 }=1
(p+q)^{2 } -4pq=1
25-4k=1
k=6

Question 7 Given that two of the zeroes of the cubic polynomial ax^{3} + bx^{2} + cx + d are 0, then find the third zero. Solution

Two zeroes = 0, 0
Let the third zero be k.
The, using relation between zeroes and coefficient of polynomial, we have:
k + 0 + 0 = -b/a
Third zero = k = -b/a

Question 8 If the zeroes of the quadratic polynomial x^{2} + (a + 1) x + b are 2 and -3, then find the value of a and b. Question 9 If one of the zeroes of the cubic polynomial x^{3} + ax^{2 }+ bx + c is -1, then find the product of the other two zeroes. Question 10 If a-b, a a+b , are zeroes of x^{3 }-6x^{2} + 8x, then find the value of b Question 11 Find a quadratic polynomial, the sum and product of whose zeroes are √2 and -3/2 respectively. Also, find its zeroes. Question 12 Given that the zeroes of the cubic polynomial x^{3} – 6x^{2} + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.

Question 13 Check whether f(x) is a factor of g(x) by dividing f(x) by g(x):
f(x) = 2x^{4} + 4x^{3} – 5x^{2} – 2x + 2, g(x) = x^{2} + 2x – 2. Question 14 Find the zeroes of the quadratic polynomial x^{2} + x -12 and verify the relationship between the zeroes and the coefficients. Question 15 If a and b are zeroes of the polynomial f(x) = 2x^{2} – 7x + 3, find the value of a^{2 }+ b^{2}. Question 16 Quadratic polynomial 4x^{2} + 12x + 9 has zeroes as p and q . Now form a quadratic polynomial whose zeroes are p -1 and q-1 Question 17 If one zero of the polynomial 2x^{2} – 5x – (2k + 1) is twice the other, find both the zeroes of the polynomial and the value of k. Question 18 If m and n are the zeroes of the quadratic polynomial f(x) = x^{2} – px + q, then find the values of:
a. m^{2 }+ n^{2}
b. m^{-1} + n^{-1} Solution

for f(x) = x^{2} – px + q
We get
m+n=p
mn=q
a) m^{2 }+ n^{2} =(m+n)^{2} -2mn= p^{2}-q
b) m^{-1} + n^{-1} = (m+n)/mn = p/q

Question 19 If the zeroes of the polynomial f(x) = x^{3} + 39x + k are in A. P., find the value of k. Question 20 Using division show that 3y^{2} + 5 is a factor of 6y^{5 }+ 15y^{4} + 16y^{3} + 4y^{2} + 10y – 35. Answer

You can use above books for extra knowledge and practicing different questions.

Note to our visitors :-

Thanks for visiting our website. From feedback of our visitors we came to know that sometimes you are not able to see the answers given under "Answers" tab below questions. This might happen sometimes as we use javascript there. So you can view answers where they are available by reloding the page and letting it reload properly by waiting few more seconds before clicking the button.
We really do hope that this resolve the issue. If you still hare facing problems then feel free to contact us using comment box given below or contact us directly by sending is an email at [email protected]
We are aware that our users want answers to all the questions in the website. Since ours is more or less a one man army we are working towards providing answers to questions available at our website.