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Chapter 2 Polynomials Ex-2.2 Interview Questions Answers

Question 1 :

Find the value ofthe polynomial (x)=5x−4x2+3 

(i) x = 0

(ii) x = – 1

(iii) x = 2

Answer 1 :

Let f(x) = 5x−4x2+3

(i) When x = 0

f(0) = 5(0)-4(0)2+3

= 3


(ii) When x = -1

f(x) = 5x−4x2+3

f(−1) = 5(−1)−4(−1)2+3

= −5–4+3

= −6


(iii) When x = 2

f(x) = 5x−4x2+3

f(2) = 5(2)−4(2)2+3

= 10–16+3

= −3

Question 2 :

Find p(0), p(1) and p(2) for each of the following polynomials:

(i) p(y)=y_2−y+1

(ii) p(t)=2+t+2t_2−t_3

(iii) p(x)=x_3

(iv) P(x) = (x−1)(x+1)


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Answer 2 :

(i) p(y)=y2−y+1

p(y) = y2–y+1

p(0) =(0)2−(0)+1=1

p(1) = (1)2–(1)+1=1

p(2) = (2)2–(2)+1=3


(ii) p(t)=2+t+2t2−t3

p(t) = 2+t+2t2−t3

p(0) =2+0+2(0)2–(0)3=2

p(1) = 2+1+2(1)2–(1)3=2+1+2–1=4

p(2) = 2+2+2(2)2–(2)3=2+2+8–8=4


(iii) p(x)=x3

p(x) = x3

p(0) =(0)= 0

p(1) = (1)= 1

p(2) = (2)= 8


(iv) P(x) = (x−1)(x+1)

p(x) = (x–1)(x+1)

p(0) =(0–1)(0+1) = (−1)(1) = –1

p(1) = (1–1)(1+1) = 0(2) = 0

p(2) = (2–1)(2+1) = 1(3) = 3

Question 3 :

Verify whether the following are zeroes of the polynomial, indicated against them.

(i) p(x)=3x+1, x=−1/3                                (ii) p(x)=5x–π, x = 4/5

(iii) p(x)=x_2−1, x=1, −1                              (iv) p(x) = (x+1)(x–2), x =−1, 2

(v) p(x) = x_2, x = 0                                     (vi) p(x) = lx+m, x = −m/l

(vii) p(x) = 3x_2−1, x = -1/√3 , 2/√3             (viii) p(x) =2x+1, x = 1/2


Answer 3 :

(i) p(x)=3x+1, x=−1/3

For, x = -1/3, p(x) = 3x+1

p(−1/3)= 3(-1/3)+1 = −1+1 = 0

-1/3is a zero of p(x).


(ii) p(x)=5x–π, x = 4/5

For, x = 4/5, p(x) = 5x–π

p(4/5)= 5(4/5)- = 4-

4/5 isnot a zero of p(x).


(iii) p(x)=x2−1, x=1, −1

For, x = 1, −1;

p(x) = x2−1

p(1)=12−1=1−1 = 0

p(−1)=(-1)2−1 = 1−1 =0

1,−1 are zeros of p(x).


(iv) p(x) = (x+1)(x–2), x =−1, 2

For, x = −1,2;

p(x) = (x+1)(x–2)

p(−1) =(−1+1)(−1–2)

= (0)(−3) = 0

p(2) = (2+1)(2–2) = (3)(0) = 0

−1,2 arezeros of p(x).


(v) p(x) = x2, x = 0

For, x = 0 p(x) = x2

p(0) = 0= 0

0 is a zero of p(x).


(vi) p(x) = lx+m, x = −m/l

For, x = -m/; p(x) = lx+m

p(-m/l)l(-m/l)+m= −m+m = 0

-m/l isa zero of p(x).


(vii) p(x) = 3x2−1, x = -1/√3 , 2/√3

For, x = -1/√3 , 2/√3 ; p(x) = 3x2−1

p(-1/√3)= 3(-1/√3)2-1 = 3(1/3)-1 = 1-1 = 0

p(2/√3) = 3(2/√3)2-1 = 3(4/3)-1 = 4−1=3 ≠ 0

-1/√3 isa zero of p(x) but 2/√3  is not a zero of p(x).


(viii) p(x) =2x+1, x = 1/2

For, x = 1/2 p(x) = 2x+1

p(1/2)=2(1/2)+1 = 1+1 = 2≠0

1/2 isnot a zero of p(x).

Question 4 :

Find the zero of the polynomials in each of the following cases:

(i) p(x) = x+5                       (ii) p(x) = x–5

(iii) p(x) = 2x+5                   (iv) p(x) = 3x–2 

(v) p(x) = 3x                         (vi) p(x) = ax, a0

(vii)p(x) = cx+d, c ≠ 0, c, d are real numbers.


Answer 4 :

(i) p(x) = x+5 

p(x) = x+5

x+5 =0

x = −5

-5 isa zero polynomial of the polynomial p(x).


(ii) p(x) = x–5

p(x) = x−5

x−5 =0

x = 5

5 is azero polynomial of the polynomial p(x).


(iii) p(x) = 2x+5

p(x) = 2x+5

2x+5 =0

2x =−5

x =-5/2

x =-5/2 is a zero polynomial of the polynomial p(x).


(iv) p(x) = 3x–2 

p(x) = 3x–2

3x−2 =0

3x = 2

x = 2/3

x = 2/3 is a zero polynomial of the polynomial p(x).


(v) p(x) = 3x 

p(x) = 3x

3x = 0

x = 0

0 is azero polynomial of the polynomial p(x).


(vi) p(x) = ax, a0

p(x) = ax

ax = 0

x = 0

x = 0is a zero polynomial of the polynomial p(x).


(vii)p(x) = cx+d, c ≠ 0, c, d arereal numbers.

p(x) = cx + d

cx+d=0

x =-d/c

x =-d/c is a zero polynomial of the polynomial p(x).


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Chapter 2 Polynomials Ex-2.2 Contributors

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