Question

check out the attachment​

Answer 1

Answer:

therefore the value of k is 5.

Answer 2

Question:

• If the roots of $5{x}^{2}+13x+k=0$ is reciprocal of other, then

• (A) k = 0
• (B) k = 5
• (C) k = 1/6
• (D) k = 6

Answer:

$\large\bold\red{(B)\:k=5}$

Step-by-step explanation:

Given,

A quadratic equation,

$5 {x}^{2} + 13x + k = 0$

Comparing the coefficient,

We have,

• a = 5
• b = 13
• c = k

Now,

Let,

• One of the root be $\bold{\alpha}$

Therefore,

• Another root will be $\bold{\frac{1}{\alpha}}$

Now,

We know that,

• Product of roots = $\frac{c}{a}$

Therefore,

We get,

$= > \alpha \times \frac{1}{ \alpha } = \frac{k}{5} \\ \\ = > \frac{k}{5} = 1 \\ \\ = > k = 5$

Hence,

The correct option is (B) k = 5