# Class 10 Maths Extra Questions for Polynomials

Given below are the Class 10 Maths Extra questions for Polynomials
a. Finding Zero's Questions
b. Short Answers Questions
c. Word Problems
d. Graph Questions

Question 1
Find a quadratic polynomial whose zeroes are $5 + \sqrt {2}$ and $5 - \sqrt {2}$

Question 2
If a and b are zeroes of quadratic polynomial $kx^2 + 4x + 4$, find the value of k such that $(a+b )^2- 2ab= 24$.

Question 3
If one zero of $3x^2 - 4x + p$ is reciprocal to the other, then find the value of p

Question 4
If p and q are the zeroes of $p(x) = kx^2 - 3x + 2k$ and $p+q=pq$ then find the value of k.

Question 5
If a and b are zeroes of $x^2 - 6x + k$. What is the value of k, if $3a+2b= 20$?

Question 6
If one zero of the quadratic polynomial $x^2 + 3x + k$ is 2, then find the value of k.

Question 7
Find the zeroes of the quadratic polynomial $x^2 + 8x + 16$ and verify the relationship between the zeroes and the coefficients.

Question 8
Find the value of a and b, if they are the zeroes of polynomial x2 + ax + b.

Question 9
If m and n are the zeroes of the polynomial $3x^2 + 11x - 4$, find the value of $\frac {m}{n} + \frac {n}{m}$

Question 10
Show that 2, -1 and 1/2 are the zeroes of the cubic polynomial
$p(x) = 2x^3 - 3x^2 - 3x + 2$

and then verify that the sum of the zeroes =-(Coeff of x2/Coeff of x3)

Question 11
Find the zeroes of the polynomial $f(x) = 4 \sqrt {3} x^2 + 5x - 2 \sqrt {3}$ , and verify the relationship between the zeroes and its coefficients.

Question 12
If p and q are the zeroes of the polynomial $f(x) = x^2 - 5x + k$ such that $p-q= 1$, find the value of k.

Question 14
If a and b are the zeroes of the quadratic polynomial $f(x) = x^2 - 4x + 3$, find the value of $a^4 b^3 + a^3 b^4$.

Question 15 If a and b are the zeroes of the quadratic polynomial $f(x) = x^2 - px + q$, prove that

Question 16
If two zeroes of the polynomial $f(x) =x^3 - 4x^2 - 3x + 12$ are √3 and -√3 then find its third zero.

Question 17
If l and m are zeroes of the polynomial $p(x) = 2x^2 - 5x + 7$, find a polynomial whose zeroes are $2l+ 3$ and $2m+ 3$.

Question 18
If p ,q and r are zeroes of polynomial $6x^3+ 3x^2 - 5x + 1$, then find the value of $\frac {1}{p} + \frac {1}{q} + \frac {1}{r}$.

Question 19
If the zeroes of the polynomial $f(x) = ax^3 + 3bx^2 + 3cx + d$ are in A. P., prove that $2b^3 - 3abc + a^2d = 0$.

Question 20
Obtain all zeroes of the polynomial $f(x) = 2x^4 - 2x^3 - 7x^2 + 3x + 6$, if its two zeros are √3/2 and -√3/2

Question 21
The graphs of y = p(x) are given in below figure, for some polynomials p(x). Find the number of zeroes of p(x), in each case.

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### Practice Question

Question 1 What is $1 - \sqrt {3}$ ?
A) Non terminating repeating
B) Non terminating non repeating
C) Terminating
D) None of the above
Question 2 The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is?
A) 19.4 cm3
B) 12 cm3
C) 78.6 cm3
D) 58.2 cm3
Question 3 The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, the AP is ?
A) 2 ,21,11
B) 1,10,19
C) -1 ,8,17
D) 2 ,11,20