determine the value of m so that the equation x^2-4x+(m-4)=0 has equal roots
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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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