Question

5. For what values of mwill the equation x2 - 2mx + 7m - 12 = 0 have (i) equal roots, (ii) reciprocal roots?​

Answer 1

Step-by-step explanation:

x2 - 2mx+ 7m - 12 = 0

(i) equal roots

a = 1 b= -2m c = 7m-12

when roots are equal then D= 0

D = b^2-4ac

0 = (-2m)^2-4×1×(7m-12)

0= 4m^2 - 28m+48

m^2-7m+12=0

m^2 - (4+3)m+12=0

m^2-4m-3m+12=0

m(m-4)-3(m-4)=0

(m-3)(m-4)=0

m = 3 m = 4

(ii) reciprocal root

let one root be a

other root be 1/a

product of roots = c/a

a × 1/a = ( 7m-12)/1

1. = 7m-12

1+12 = 7m

13/7 = m