Question

4x²-17x+ k = 0 has the reciprocal roots.​

Answer 1

Answer: k=4

Explanation:

4x²-17x+k=0

Divide both parts of the equation by 4:

`\displaystyle\\(4x^2)/(4)-(17x)/(4)+(k)/(4)=0\\\\x^2-(17)/(4) x +(k)/(4) =0\\`

Let one of the roots of this equation be α

Then the other root of this equation is 1/α

Hence,

`\displaystyle\\\alpha ((1)/(\alpha ))=(k)/(4) \\\\(\alpha )/(\alpha )= (k)/(4) \\\\1=(k)/(4)`

Multiply both parts of the equation by 4:

4=k

Thus, k=4