Question

Find k for which the roots of (k - 9 )x² + 2 (k - 9 ) x + 4 = 0 have equal roots

Answer 1

Answer:

given quadratic equation = ( k - 9)x² + 2( k - 9) x + 4 = 0

here

a = k - 9

b = 2( k - 9)

c = 4

we know

for equal roots,

b² - 4ac = 0

=> b² = 4ac

=> [2( k - 9)]² = 4( k - 9)*4

=> 4( k - 9)² = 16( k - 9)

=> ( k - 9)² = 4( k - 9)

=> ( k - 9)² - 4( k - 9) = 0

=> (k - 9) [ (k - 9) - 4 ] = 0

=> (k - 9) = 0 , or [ k - 13] = 0

=> k = 9 or k = 13

Answer 2

K = 9 or k = 13 is the correct answer.