Question

if the sum of the cubes of zeroes of the polynomial x³ -5x²+k²x+8 is 71 then √k can be​

Answer 1

sum of the cubes of zeroes of the polynomial x³ -5x²+k²x+8 is 71  then K = √2

Step-by-step explanation:

x³ -5x²+k²x+8

if  p  , q  , r  are roots then

p + q + r  = 5

pqr = -8

pq+pr+qr = k²

(p + q + r)³ = p³ + q³ + r³   + 3 (p + q)(q + r) (p + r)

=> 5³ = 71 + 3(5 - r)(5 - p)(5 - q)

=> 125 = 71 + 3 ( 25 + pr - 5p - 5r)(5 - q)

=> 54 = 3 ( 125 - 25q + 5pr - pqr - 25p +5pq - 25r + 5qr)

=> 18 =  125 - 25(P + q + r) - pqr + 5 (pq + pr + qr)

=> 18 = 125 - 25*5  + 8 + 5k²

=> 5k² = 10

=> k² = 2

=> k = √2