Class 10 Maths Extra Questions for Polynomials

Given below are the Class 10 Maths Extra questions for Real Numbers
a) Finding Zero's Questions
c) Word Problems

Question 1) Find a quadratic polynomial whose zeroes are 5 +  √2 and 5 -√2
Question 2) If  a and b are zeroes of quadratic polynomial kx2 + 4x + 4, find the value of k such that (a+b )2 - 2ab  = 24.
Question 3) If one zero of 3x2 – 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) = kx2 – 3x + 2k and p+q=pq  then find the value of k.
Question 5) If  a and b are zeroes of x2 – 6x + k. What is the value of k, if 3a+2b  = 20?
Question 6) If one zero of the quadratic polynomial x2 + 3x + k is 2, then find the value of k.
Question 7) Find the zeroes of the quadratic polynomial x2 + 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 3x2 + 11x – 4, find the value of (m/n)  +(n/m)
Question 10) Show that 2, -1 and 1/2  are the zeroes of the cubic polynomial
p(x) = 2x3 – 3x2 – 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√3  x2 + 5x - 2√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) = x2 – 5x + k such that p-q  = 1, find the value of k.
Question 13) If p and q are the zeroes of the quadratic polynomial f(x) = kx2 + 4x + 4 such that  p2 + q2  = 24, find the values of k.

Question 14) If  a and b are the zeroes of the quadratic polynomial f(t) = x2 – 4x + 3, find the value of a4 b3 + a3 b4.
Question 15) If a and b  are the zeroes of the quadratic polynomial f(x) = x2 – px + q, prove that

Question 16) If two zeroes of the polynomial f(x) = x3 – 4x2 – 3x + 12 are √3 and -√3  then find its third zero.
Question 17) If  l and m are zeroes of the polynomial p(x) = 2x2 – 5x + 7, find a polynomial whose zeroes are 2l + 3 and 2m  + 3.\
Question 18) If p ,q and r are zeroes of polynomial 6x3 + 3x2 – 5x + 1, then find the value of p-1 + q-1 + r-1.
Question 19)  If the zeroes of the polynomial f(x) = ax3 + 3bx2 + 3cx + d are in A. P., prove that 2b3 – 3abc + a2d = 0.
Question 20) Obtain all zeroes of the polynomial f(x) = 2x4 – 2x3 – 7x2 + 3x + 6, if its two zeros are √3 and -√3