যদি দুটা শূণ্য√⅗আৰু-√⅗তেন্তে 3x⁴+6x³-2x²-10x-5 ৰ বাকী আটাইবোৰ শূণ্য উলিওৱা|
Answers
Correct Question :- Obtain all the zeros of the polynomial 3x^4 + 6x^3 – 2x^2 – 10x – 5, if two of its zeros are √5/3 and (-√5/3) ?
Solution :-
since two roots of the given polynomial are √5/3 and -√5/3.
So, (x - √5/3) * (x + √5/3) is a factor of given polynomial .
then,
→ (x - √5/3) * (x + √5/3)
→ x² - (5/3)
now dividing the given polynomial by (x² - 5/3) we get,
x² - 5/3 ) 3x⁴ + 6x³- 2x²- 10x - 5 ( 3x² + 6x + 3
3x⁴ - 5x²
6x³ + 3x² - 10x
6x³ - 10x
3x² - 5
3x² - 5
0
then, finding factors of quotient now,
→ 3x² + 6x + 3 = 0
→ 3(x² + 2x + 1) = 0
→ x² + 2x + 1 = 0
→ (x + 1)² = 0
→ x = (-1) and (-1)
therefore, all the zeros of the polynomial are √5/3 , (-√5/3) , (-1) and (-1) .
Learn more :-
JEE mains Question :-
https://brainly.in/question/22246812
. Find all the zeroes of the polynomial x4
– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.
https://brainly.in/question/39026698