Obtain all other zeros of x 4 + 4 x cube minus 2 x square - 20 x minus 15 if two of its zeros are under root 5 and minus under root 5
Answers
Other zeroes are -1 & - 3 if √5 & - √5 are zeroes of x⁴ + 4x³ - 2x² -20x - 15 = 0
Step-by-step explanation:
x⁴ + 4x³ - 2x² -20x - 15 = 0
two of its zeros are √5 & -√5
so (x - √5)(x + √5) are factor of x⁴ + 4x³ - 2x² -20x - 15
=> (x² - 5) is factor of x⁴ + 4x³ - 2x² -20x - 15
x² + 4x + 3
x²-5 _| x⁴ + 4x³ - 2x² -20x - 15 |_
x⁴ -5x²
_______________
4x³ + 3x² - 20x - 15
4x³ -20x
____________________
3x² - 15
3x² - 15
____________
0
_____________
x² + 4x + 3 is also one of the factor
x² + 4x + 3 = 0
=> x² + 3x + x + 3 = 0
=> x(x + 3) + 1(x + 3) =0
=> (x + 1)(x + 3) = 0
=> x = - 1 or - 3
Other zeroes are -1 & - 3
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Answer:
it is the answer
hope it would be helpful
