Q11 of 227 Page 114

If one root of the equation 2x2 – ax + 64 = 0 is twice the other, then find the value of a

Roots of any quadratic equation are α and β


Here one root is twice the other.


α = 2β


by comparing the given equation with general form of quadratic equation we get,


a = 2, b = –a and c = 64






α + β =



…(1)


αβ = 32


2β(β) = 32


2β2 = 32


⇒


⇒ β2 = 16


⇒ β = √16


⇒ β =± 4



⇒


⇒


⇒ 12 × 2 = a


⇒ a = 24


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