Question

if one root of the equation2x^2-ax+64 is twice the other,find the value of a

Answer 1

Heya !!



P(X) = 2X² - AX + 64



Here,



Coefficient of X² = 2


Coefficient of X = -A


And,


Constant term = 64




Let one zero of the given quadratic polynomial be Alpha .



Other zero = 2Alpha




Therefore,

Product of zeroes = Constant term/Coefficient of X².



Alpha × 2Alpha = 64/2



2Alpha² = 32


Alpha² = 16



Alpha = ✓16 = (+4) or (-4)



And,


Sum of zeroes = -(Coefficient of X)/Coefficient of X²




Alpha + 2Alpha = -(-a)/2



4 + 2 × 4 = a/2




4 + 8 = a/2





a = 12 × 2



A = 24 .

Answer 2

Hi dear

★ Here is your answer★

P(X) = 2X² - AX + 64

suppose one zero of the given quadratic polynomial be Alpha .

Other zero = 2Alpha

Product of zeroes = C/a

Alpha*2Alpha = 64/2

2alpha² = 32

alpha = ✓16 = 4

sum of zeroes = -b/a

Alpha + 2Alpha = -(-a)/2
4 + 2*4= a/2
a = 12 × 2
a= 24