Class X : HOTS Question Answers: Math Unit - 2 (Polynomials)

POLYNOMIALS

It is not once nor twice but times without number that the same ideas make their appearance in the world

1. If two zeros of the polynomial f(x) = x4 - 6x3 - 26x2 + 138x – 35 are 2 3.Find the other zeros. (Ans:7, -5)
2. Find the Quadratic polynomial whose sum and product of zeros are 2 + 1, .
3. If , are the zeros of the polynomial 2x2 – 4x + 5 find the value of a) 2 +  2 b) ( - )2.
4. If , are the zeros of the polynomial x2 + 8x + 6 frame a Quadratic polynomial whose zeros are a) and b) 1 + , 1 + .
5. On dividing the polynomial 4x4 - 5x3 - 39x2 - 46x – 2 by the polynomial g(x) the quotient is x2 - 3x – 5 and the remainder is -5x + 8.Find the polynomial g (x). (Ans:4 x2+7x+2)
6. If the squared difference of the zeros of the quadratic polynomial x2 + px + 45 is equal to 144 , find the value of p.
7. If , are the zeros of a Quadratic polynomial such that  +  = 24,  -  = 8. Find a Quadratic polynomial having  and  as its zeros.
8. If  & ß are the zeroes of the polynomial 2x2 ─ 4x + 5, then find the value of
9.  2 + ß2 b. 1/  + 1/ ß c. ( ─ ß)2 d. 1/2 + 1/ß2 e. 3 + ß3
10. Obtain all the zeros of the polynomial p(x) = 3x4 ─ 15x3 + 17x2 +5x ─6 if two zeroes are ─1/√3 and 1/√3.