Question

If 2 is a root of the equation 2 + + 12 = 0 and the equation 2 + + q = 0 has equal roots then find the value of .

Answer 1

q= 16

Step-by-step explanation:

Solution

x²+kx+12=0

root of the above equation is 2

2² +k(2)+12=0

4+2k+12=0

2k=−16

k=−8

x² +kx+q=0

x ²−8x+q=0

condition for equal roots is b² =4ac

∴(−8) ² =4(1)(q)

64=4q

∴q=16

Answer 2

Step-by-step explanation:

x

2

+kx+12=0

root of the above equation is 2

2

2

+k(2)+12=0

4+2k+12=0

2k=−16

k=−8

x

2

+kx+q=0

x

2

−8x+q=0

condition for equal roots is b

2

=4ac

∴(−8)

2

=4(1)(q)

64=4q

∴q=16