If the roots of the equation x2 - 8x + a2 - 6a = 0 are real and distin

1.	If the roots of the equation x2 - 8x + a2 - 6a = 0 are real and distinct, then find all possible values of a.
Answer» Since the roots of the given equation are real and distinct, we must have D > 0 => 64 - 4 (a² - 6a) > 0 => 4[16 - a² + 6a] > 0 => -4(a² - 6a - 16) > 0 => a² - 6a - 16 < 0 => (a - 8) (a + 2) < 0 => - 2 < a < 8 Hence, the roots of the given equation are real if ‘a’ lies between -2 and 8.

If the roots of the equation x2 - 8x + a2 - 6a = 0 are real and distinct, then find all possible values of a.

Answer»

Since the roots of the given equation are real and distinct, we must have D > 0

=> 64 - 4 (a² - 6a) > 0

=> 4[16 - a² + 6a] > 0

=> -4(a² - 6a - 16) > 0

=> a² - 6a - 16 < 0

=> (a - 8) (a + 2) < 0

=> - 2 < a < 8

Hence, the roots of the given equation are real if ‘a’ lies between -2 and 8.