find K for which sum and the product of roots of a quadratic equation kX square - 4 x + 4 K=0 are equal
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Let the quadratic equation be,
ax² + bx + c = 0
a = k, b = -4, c = 4k
let the zeroes be m and n
sum of zeroes = -b/a
m + n = 4/k
product of zeroes = c/a
x × y= 4k/k
According to question
sum of zeroes = product of zeroes
So,
m + n = m × n
or 4/ k = 4k/ k
or 4/ k = 4/ 1
or 1/ k = 4/ 4
or 1/ k = 1/ 1
or k = 1
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