**Notes**
**NCERT Solutions**
**Assignments**
**Revision Notes**
Given below are the Class 10 Maths Extra questions for Real Numbers

a) Finding Zero's Questions

b) Short Answers 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 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 x

^{2} + ax + b.

**Question 9)** If m and n are the zeroes of the polynomial 3x

^{2 }+ 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) = 2x

^{3} – 3x

^{2} – 3x + 2

and then verify that the sum of the zeroes =-(Coeff of x

^{2}/Coeff of x

^{3})

**Question 11)** Find the zeroes of the polynomial f(x) = 4√3 x

^{2} + 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) = x

^{2} – 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) = kx

^{2 }+ 4x + 4 such that p

^{2} + q

^{2} = 24, find the values of k.

**Question 14)** If a and b are the zeroes of the quadratic polynomial f(t) = 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 p

^{-1} + q

^{-1} + r

^{-1}.

**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

^{2}d = 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 and -√3

Answer
1) x^{2} – 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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Class 10 Maths
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