Question

the sum of zeroes for the cubic polynomial 4x³-5x²-7 is​

Answer 1

Answer:

if two zeros ( 2 +√3) and ( 2 -√3) are given of polynomial it means

{ x -(2 -√3)} and { x -( 2+√3) } are the factors of given polynomial ,

hence,

{ x -(2 -√3)}{x -(2+√3)} is a factor of given polynomial .

{ x² -(2+√3)x -(2-√3)x +(2-√3)(2+√3)} is a factor of given polynomial .

{ x²-(4)x + 1} is a factor of given polynomial .

hence, x²-4x +1 is divisible by given polynomial .

now,

x² -4x +1 ) 2x⁴ -9x³+ 5x² +3x -1( 2x²-x -1

2x⁴ -8x³ +2x²

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-x³ +3x² +3x

-x³ +4x² -x

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-x² + 4x -1

-x² +4x -1

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0000

so, 2x² -x -1 is a factor in which two unknown roots present

now,

2x² -x -1 =0

2x² -2x +x -1 =0

2x( x -1)+ ( x -1) = 0

(2x +1)( x -1)=0

x = -1/2 and 1

so, -1/2 and 1 are two unknown roots of given polynomial .

Step-by-step explanation: