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Class 10 Maths Problems for Polynomial



1) Find a quadratic polynomial whose zeroes are 5 +  √2 and 5 -√2
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.
3) If one zero of 3x2 – 4x + p is reciprocal to the other, then find the value of p
4) If  p and q are the zeroes of p(x) = kx2 – 3x + 2k and p+q=pq  then find the value of k.
5) If  a and b are zeroes of x2 – 6x + k. What is the value of k, if 3a+2b  = 20?
6) If one zero of the quadratic polynomial x2 + 3x + k is 2, then find the value of k.
7) Find the zeroes of the quadratic polynomial x2 + 8x + 16 and verify the relationship between the zeroes and the coefficients.
8) Find the value of a and b, if they are the zeroes of polynomial x2 + ax + b.
9) If m and n are the zeroes of the polynomial 3x2 + 11x – 4, find the value of (m/n)  +(n/m)
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)
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.
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.
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.
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.
15) If a and b  are the zeroes of the quadratic polynomial f(x) = x2 – px + q, prove that

16) If two zeroes of the polynomial f(x) = x3 – 4x2 – 3x + 12 are √3 and -√3  then find its third zero.
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.\
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.
19)  If the zeroes of the polynomial f(x) = ax3 + 3bx2 + 3cx + d are in A. P., prove that 2b3 – 3abc + a2d = 0.
20) Obtain all zeroes of the polynomial f(x) = 2x4 – 2x3 – 7x2 + 3x + 6, if its two zeros are √3 and -√3
Answer
1) x2 – 10x + 21
2) 2/3,-1
3) p=3
4) k=3/2
6) -16
7) -4 and -4
8) a=1 and b=-2
9) -145/12
11) -2/ √3, √3/4
12) 6
13) -1,2/3
14) 108

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