Obtain all other zeroes of polynomial 2x4+3x³-5x²-9x-3, if 2 of its zeros are √3 and -√3
Answers
Answer:
the other zeroes are -1/2 and -1
Step-by-step explanation:
given polynomial : 2x⁴+3x³-5x²-9x-3
2 of its zeroes are +√3 and -√3
let the zeroes be (x+√3)(x-√3)
hence zeroes = x²-(√3)²
=x²-3
now dividing polynomial by x²-3..
x²-3) 2x⁴+3x³-5x²-9x-3 ( 2x²+3x+1
2x⁴ -6x²
⁽⁻⁾ ⁽⁺⁾
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
3x³+ x²-9x
3x -9x
⁽⁻⁾ ⁽⁺⁾
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
x²-3
x²-3
⁽⁻⁾ ⁽⁺⁾
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
0 0
now factorising, 2x²+3x+1
2x²+2x+1x+1
2x(x+1)+1(x+1)
(2x+1)(x+1)=0
2x+1=0 x+1=0
2x= -1 x= -1
x = -1/2
therefore other zeroes are -1/2 and -1
hope its correct
mark me as brainliest
Answer:
the other zeroes are -1/2 and -1
given polynomial : 2x⁴+3x³-5x²-9x-3
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²=x²-3
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²=x²-3now dividing polynomial by x²-3..
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²=x²-3now dividing polynomial by x²-3..x²-3) 2x⁴+3x³-5x²-9x-3 ( 2x²+3x+1
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²=x²-3now dividing polynomial by x²-3..x²-3) 2x⁴+3x³-5x²-9x-3 ( 2x²+3x+1 2x⁴ -6x²
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²=x²-3now dividing polynomial by x²-3..x²-3) 2x⁴+3x³-5x²-9x-3 ( 2x²+3x+1 2x⁴ -6x² ⁽⁻⁾ ⁽⁺⁾
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²=x²-3now dividing polynomial by x²-3..x²-3) 2x⁴+3x³-5x²-9x-3 ( 2x²+3x+1 2x⁴ -6x² ⁽⁻⁾ ⁽⁺⁾ 3x³+ x²-9x
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²=x²-3now dividing polynomial by x²-3..x²-3) 2x⁴+3x³-5x²-9x-3 ( 2x²+3x+1 2x⁴ -6x² ⁽⁻⁾ ⁽⁺⁾ 3x³+ x²-9x 3x -9x
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²=x²-3now dividing polynomial by x²-3..x²-3) 2x⁴+3x³-5x²-9x-3 ( 2x²+3x+1 2x⁴ -6x² ⁽⁻⁾ ⁽⁺⁾ 3x³+ x²-9x 3x -9x ⁽⁻⁾ ⁽⁺⁾
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²=x²-3now dividing polynomial by x²-3..x²-3) 2x⁴+3x³-5x²-9x-3 ( 2x²+3x+1 2x⁴ -6x² ⁽⁻⁾ ⁽⁺⁾ 3x³+ x²-9x 3x -9x ⁽⁻⁾ ⁽⁺⁾ x²-3
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²=x²-3now dividing polynomial by x²-3..x²-3) 2x⁴+3x³-5x²-9x-3 ( 2x²+3x+1 2x⁴ -6x² ⁽⁻⁾ ⁽⁺⁾ 3x³+ x²-9x 3x -9x ⁽⁻⁾ ⁽⁺⁾ x²-3 x²-3
given polynomial : 2x⁴+3x³-5x²-9x-32 of its zeroes are +√3 and -√3let the zeroes be (x+√3)(x-√3)hence zeroes = x²-(√3)²=x²-3now dividing polynomial by x²-3..x²-3) 2x⁴+3x³-5x²-9x-3 ( 2x²+3x+1 2x⁴ -6x² ⁽⁻⁾ ⁽⁺⁾ 3x³+ x²-9x 3x -9x ⁽⁻⁾ ⁽⁺⁾ x²-3 x²-3 ⁽⁻⁾ (+)
0 0
0 0now factorising, 2x²+3x+1
0 0now factorising, 2x²+3x+12x²+2x+1x+1
0 0now factorising, 2x²+3x+12x²+2x+1x+12x(x+1)+1(x+1)
0 0now factorising, 2x²+3x+12x²+2x+1x+12x(x+1)+1(x+1)(2x+1)(x+1)=0
0 0now factorising, 2x²+3x+12x²+2x+1x+12x(x+1)+1(x+1)(2x+1)(x+1)=02x+1=0 x+1=0
0 0now factorising, 2x²+3x+12x²+2x+1x+12x(x+1)+1(x+1)(2x+1)(x+1)=02x+1=0 x+1=02x= -1 x= -1
0 0now factorising, 2x²+3x+12x²+2x+1x+12x(x+1)+1(x+1)(2x+1)(x+1)=02x+1=0 x+1=02x= -1 x= -1x = -1/2
0 0now factorising, 2x²+3x+12x²+2x+1x+12x(x+1)+1(x+1)(2x+1)(x+1)=02x+1=0 x+1=02x= -1 x= -1x = -1/2therefore other zeroes are -1/2 and -1
0 0now factorising, 2x²+3x+12x²+2x+1x+12x(x+1)+1(x+1)(2x+1)(x+1)=02x+1=0 x+1=02x= -1 x= -1x = -1/2therefore other zeroes are -1/2 and -1hope its correct