Question

Find the zeros of polynomial x cube minus 5 x square - 16 X + 80 if its two zeros are equal in magnitude but opposite in in signe sign

Answer 1

Solution :-

x³ - 5x² - 16x + 80

Firstly Factorise is :-

-> x³ - 16x - 5x² + 80

-> x (x² - 16) - 5 (x² - 16)

-> (x ² - 16) (x - 5)

-> (x² - 4²) (x - 5)

Identity :- (a² - b²) = (a+ b) (a - b)

-> (x + 4) (x - 4) (x - 5)

-> (x + 4) = 0

-> x = -4

-> (x - 4) = 0

-> x = 4

-> (x - 5) = 0

-> x = 5

The zeroes of x³ - 5x² - 16x + 80 are 4, -4, 5.

So, the zeroes which are equal in magnitude but opposite in signs are 4 and -4.

Answer 2

x³ - 5x² - 16x + 80

________ [GIVEN EQUATION]

• We have to find zeros of the above equation.

______________________________

=> x³ - 5x² - 16x + 80 = 0

=> x²(x - 5) - 16(x - 5) = 0

=> (x² - 16) (x - 5) = 0

=> x² - 16 = 0

=> x² = 16

=> x = √16

=> x = ± 4

• Similarly

=> x - 5 = 0

=> x = + 5

______________________________

+4, -4 and +5 are the zeros of the polynomial x³ - 5x² - 16x + 80

_________ [ANSWER]