ncert cbse 10th chapter 2 exercise 2.3
3. obtain all other zeroes of 3(x^4)+6(x^3)-2(x^2)-10x-5 if two of its zeroes are sqrt(5/3) and [sqrt(5/3)]
factors are
[x-sqrt(5/3)][x-sqrt(5/3)] = [(x^2) - (5/3)]=(1/3) [3(x^2) -5]
now divide the given expression 3(x^4)+6(x^3)-2(x^2)-10x-5 with [3(x^2) -5]
using long division
(x^2) +2x +1
---------------------------------------------------------------------------
3(x^2)+0x -5 | 3(x^4)+6(x^3)- 2(x^2) - 10x -5
| 3(x^4)+0(x^3) -5(x^2)
-------------------------------------------------------------------
| 6(x^3) +3(x^2)- 10x
| 6(x^3) +0(x^2) - 10x
-----------------------------------------------------------------
| 3(x^2) +0x -5
| 3(x^2) +0x -5
-------------------------------------------------------------
| 0
and –2x + 4, respectively. Find g(x).
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ncert cbse 10th mathematics chapter 2 optional exerciseIf the zeroes of the polynomial (x^3) – 3(x^2) + x + 1 are a – b, a, a + b, find a and b.
solution
2. Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively
solution
4. If two zeroes of the polynomial (x^4) – 6(x^3) – 26(x^2) + 138x – 35 are
[2 ±sqrt(3) ] , find other zeroes
solution
5. If the polynomial (x^4) – 6(x^3) + 16(x^2) – 25x + 10 is divided by another polynomial (x^2) – 2x + k, the remainder comes out to be x + a, find k and a
solution
exercise 2.3
3. obtain all other zeroes of 3(x^4)+6(x^3)-2(x^2)-10x-5 if two of its zeroes are sqrt(5/3) and [sqrt(5/3)]
solution
4. On dividing (x^3) – 3(x^2) + x + 2 by a polynomial g(x), the quotient and remainder were x – 2
and –2x + 4, respectively. Find g(x).
solution
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