Question

if one root of 3x^2+11x+k=0 be reciprocal of other, find value of K? ​
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Answer 1

Answer:

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Answer 2

Given: One root of $3 {x}^{2} + 11x + k = 0$ is reciprocal of the other root.

To find: The value of k

Solution: Let one root of this quadratic equation be a.

Since the other root is a reciprocal of the other, the this root, the other root= 1/a

Product of these roots

= a × 1/a

=1

Now, in a quadratic equation $a {x}^{2} + bx + c = 0$,

the product of the roots = c/a

Here, a=3, b=11 and c=k

Therefore,

Product of roots is

= c/a

=k/3

But product of roots=1

Therefore,

k/3=1

=> k = 1 × 3

=> k = 3

Therefore, the value of k is 3.