Question

If a and b are the roots of the equation

${x}^{2} - kx + 16 = 0$ and satisfy
${a}^{2} + {b}^{2} = 32$
, then the value of
is
A) -8
B) -8,8
C) 6
D) 10​

Answer 1

Step-by-step explanation:

x² -kx +16 = 0

a and b are roots...

a+b = k

ab = 16

(a+b)² = a² + b² + 2ab

(a+b) ² = k²

a² + b² = 36

a² + b² + 2ab - 2ab = 36

(a+b) ² - 2ab = 36

k² - 2(16) = 36

k² = 36 + 32

k² = 68

k ~ -8 and +8

Answer 2

Answer:

x² -kx +16 = 0

a and b are roots...

a+b = k

ab = 16

(a+b)² = a² + b² + 2ab

(a+b) ² = k²

a² + b² = 36

a² + b² + 2ab - 2ab = 36

(a+b) ² - 2ab = 36

k² - 2(16) = 36

k² = 36 + 32

k² = 68

k ~ -8 and +8