Question

if alpha beta are roots of x square + 5 x + K is equals to zero and Alpha square beta + alpha beta square is equals to minus 30 then find k​

Answer 1

Answer:

6

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Answer 2

The value of k is $- \frac{5}{2}$.

Step-by-step explanation:

The given quadratic equation is $x^{2} + 5x + k = 0$.

and $\alpha^{2} + \beta^{2}$ = - 30

To find, k = ?

∴ α + β = $-\frac{b}{a} = - 5$

and  α·β = $\frac{c}{a} = k$

∴ $\alpha^{2} + \beta^{2}$ = $(\alpha + \beta)^{2} -2\alpha\beta$

⇒ 25 - 2k = 30

⇒  - 2k = 30 - 25 = 5

⇒ k = $- \frac{5}{2}$

Hence, the value of k is $- \frac{5}{2}$.