1.

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

Answer»

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 .


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