Question

Determine the value of ‘m’ so that the equation x – 4x + (m – 4) = 0 has equal roots

Answer 1

Step-by-step explanation:

if roots are equal means

b²-4ac=0

Answer 2

Given :  x² - 4x   + (m - 4) = 0  has equal roots

To find : Value of m

Solution:

x² - 4x   + (m - 4) = 0

Let say Equal Roots are a

=> (x - a)(x - a) = 0

=> x² - 2ax  + a² = 0

Comparing

with

x² - 4x   + (m - 4) = 0

=> 2a = 4  => a = 2

a² = m - 4

=> 2² = m - 4

=> 4 = m - 4

=> m = 8

and roots are 2 , 2

Another Way

ax² + bx  + c = 0

Has equal roots if

b² - 4ac = 0

Comparing

x² - 4x   + (m - 4) = 0   with ax² + bx  + c = 0

a = 1   , b = - 4  , c  = m - 4

(-4)² - 4(m - 4) = 0

=>  16 = 4(m - 4)

=> 4 = m - 4

=> m = 8

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