Question

If α and β are roots of the equation
X^2-px+16 satisfy relation α^2+β^2=9 write value of p

Answer 1

Heya !!

P ( X ) = X² - PX + 16




Here,



A = Coefficient of X² = 1



B = Coefficient of X = -P


And,


C = Constant term = 16






Sum of zeroes = -B/A




Alpha + Beta = -(-P) /1



Alpha + Beta = P ---------(1)



And,


Product of zeroes = C/A



Alpha × Beta = 16 --------(2)




Given that : (Alpha)² + (Beta)² = 9






=> ( Alpha - Beta )² + 2Alpha Beta = 9




=> (P)² + 2 × 16 = 9





=> P² = 9 - 32




=> P² = -23




=> P = ✓-23