Question

find the least integral value of k for which the equation x²-2(k+2)x+12+k² has real and distinct roots.
thank you​

Answer 1

Answer:

3

Step-by-step explanation:

For roots to be real and distinct, D>0

D>0

b²-4ac>0

(-2(k+2))²-4(12+k²)>0

4(k+2)²-48-4k²>0

4(k²+4+4k)-48-4k²>0

4k²+16+16k-48-4k²>0

16k-32>0

16k>32

k>2

Least integral value = 3

Answer 2

Answer:

3

Step-by-step explanation:

for roots to be real and distinct,

DISCRIMINANT MUST BE GRATER THAN 0.

D>0

D= b² - 4ac

here b= -2(k+2)

a=1

c= 12+ k²

so, D= (-2)².(k+2)² -4(1)(12+k²) >0 [(a+b)²= a² + b² + 2ab]

4(k² + 4 + 4k) + 4(-12 - k²) >0 [×¼]

k² + 4 + 4k -12 -k² >0

4k -8 >0

4k > 8

k > 8/4

k>2

Least integral value of k=3