Question

please help me to find out this
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Answer 1

2 is the answer

please see attached photo for detailing

Answer 2

Question:-

$\sf \large If \alpha, \beta \: be \: the \: zeros \:of \: the \: polynomial \\ \sf \large 2x {}^{2} + 5x + k \: such \: that \: \alpha {}^{2} + \beta {}^{2} + \alpha \beta = \frac{21}{4} \: then \: k = ?$

Given:-

That α and β are the zeros of polynomial.

To Find:-

• Value of k.

Solution:-

Hence, we have

$\sf \large \alpha + \beta = - \frac{5 }{2} \: \: \: ...(i)$

$\sf \large \alpha \beta = \frac{k}{2} \: \: \: ...(ii)$

Now, we have been given that

$\sf \large\alpha {}^{2} + \beta {}^{2} + \alpha \beta = \frac{21}{4}$

We can rewrite this question as

$\sf \large( \alpha + \beta) {}^{2} - \alpha \beta = \frac{21}{4}$

Using the equation (i) and (ii)

$\sf \large( - \frac{5}{2} ) {}^{2} - \frac{k}{2} = \frac{21}{4}$

$\sf \large \longmapsto \frac{k}{2} = \frac{25}{4} - \frac{21}{4}$

$\sf \large \longmapsto \frac{k}{2} = 1$

$\sf \large \longmapsto k = 2.$

Answer:-

${ \boxed{ \sf \large \blue{ \therefore The \: value \: of \: k = \underline{ 2.}}}}$

Hope you have satisfied. ⚘