Question

If one zero of the quadratic polynomial p(x) = 5x + 13x - kis the reciprocal of other, the value of k is
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Answer 1

Answer:

$\large\boxed{\sf{k=-5}}$

Step-by-step explanation:

Given that there is a quadratic polynomial,

$p(x) = 5 {x}^{2} + 13x - k$

It's also given that the zeroes are reciprocal of each other.

Let, one of the zeroes is $\bold{\alpha}$

Therefore, other zero will be $\bold{\dfrac{1}{\alpha}}$

Now, we know that,

Sum of zeroes =$- \dfrac{coeff.\; of\; x}{coeff.\;of\;{x}^{2}}$

Product of zeroes = $\dfrac{constant\;term}{coeff.\;of\;{x}^{2}}$

Therefore, we will get,

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

Hence, the required value of k = -5