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Given quadratic equation:

kx² – 14x + 8 = 0

We know that roots of a quadratic equation ax² + bx + c, a ≠ 0 are

For given equation:

a = k

b = –14

c = 8

Let the roots of above equation be α and β

Given that,

One root is six times other, therefore

α = 6β

Applying the formula, we get

Squaring both side,

196 – 32k =100

⇒ 32k = 96

⇒ k = 3