Question

18. For each equation, given below, find the
value of 'm' so that the equation has
equal roots. Also, find the solution of each
equation :
(i) (m - 3)x2 - 4x + 1 = 0)
( 7) = 0
​

Answer 1

Heya!

FOR EQUAL ROOTS DESCRIMNANT = 0

GIVEN QUADRATIC EQUATION IS

( m - 3 )x² - 4x + 1 = 0

it's Descrimnant ( D ) is given by

D = ( -4 )² - 4 ( m - 3 ) ( 1 )

D = 0 For equal roots.

16 - 4m + 12 = 0

28 - 4m = 0

4m = 28

m = 7

=>

Now, put value of m in given Equation to get original Equation.

( 7 - 3 )x² - 4x + 1 = 0

4x² - 4x + 1 = 0

4x² - 2x - 2x + 1 = 0

2x ( 2x - 1 ) -1 ( 2x - 1 ) = 0

( 2x - 1 ) = 0 OR ( 2x - 1 ) =0

x = 1/2