Question

If alpha and beta are the zeros of polynomial p(x)= 6x^2-5x+k find the value of k if 1/alpha + 1/beta = 5

Answer 1

Answer:

k = 1

Step-by-step explanation:

$\frac{1}{\alpha} + \frac{1}{\beta} = 5$ (given)

$\frac{\alpha + \beta}{\alpha\beta} = 5$ (taking LCM)

But, $\alpha + \beta = -\frac{b}{a}$ and $\alpha\beta = \frac{c}{a}$

Here, $\alpha + \beta = \frac{5}{6}$

And $\alpha\beta = \frac{k}{6}$

Substituting these in the (simplified) given equation, we get:

$\frac{\frac{5}{6}}{\frac{k}{6}} = 5$

Or, $\frac{5}{k} = 5$

So, $k = 1$

Answer 2

K=1

Step-by-step explanation:

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