Class 10 Polynomial Test paper

1. If x=1 is a zero of a polynomial f(x) = x³-2x²+4x+k. Write the value of k                        (Ans. k= -3)

2. For what value of k , -4 is a zero of the p(x)=. x² – x - (2k+2) ?  (Ans. = 9)

3. Verify whether 3 and 2 are the zeros of the poly. (x - 2)(x -3)?

4. Find the zeros of the polynomial f(x) =4x²+8x               (Ans. 0, -2)

5. Find a quadratic polynomial each with the given zeros as sum and the product of its zeros respectively      

(a) ¼, -1              (b) √2  , 1/3                                       
{Ans.(a).4x²-x-4,(b) 3x²-3√2 x+1}

3 marks questions

1. Using division algorithm, find the quotient and the remainder on dividing f(x) by g(x) , where

f(x) =6x³ +13x² + x - 2 and g(x) =2x+1                                              

[Ans.q (x) =3x²+5x-2, r(x)=0]

2. If α , β are the zeros of 2y2+7y+5 write the value of α+ β +α β.   
(Ans. -1)

3. Find the zeros of a quadratic polynomial 5x2-4-8x and verify the relationship between the zeros and the coefficients of the polynomial.                                                                                            (Ans.2,-2/5 )

4. If α, β are the zeros of the poly. f(x)=x²-px+q, find the value of  (a) α²+β²       (b)1/α +1β        

(Ans. P² -2q, p/q ) 

5. On dividing x³+2x²-5x-6 by a polynomial g(x) the quotient and remainder were x+1 and - 4x -4 respectively Find the polynomial g(x)      

(Ans. x²+ x - 2)

6. If (x + a) is a factor of 2x²+2ax+5x+10. Find a.              (Ans. a = 2)

7. Find all the zeros of 2x⁴-9x³+5x²+3x-1, if two of its zeros are 2+√3 & 2- √3

8. If the polynomial 6x⁴ + 8x³ + 17x² + 21x + 7 is divided by another polynomial 3x² + 4x + 1, the remainder comes out to be (ax + b), find a and b.

9. Find all other zeroes of the polynomial p(x) = 2x³ + 3x² – 11x – 6, if one of its zero is –3.

10. If one zero of the polynomial (a² +9)x² +13x +6a is reciprocal of the other . Find the value of a.