Question

${x}^{3} - 6 {x}^{2} - x + \: 30 =0 \\ is \: a \: polynomail \: .if \: the \: zeros \: \: \: \: \\ are \: \: \: \: \: \alpha \: \: \beta \: \: \: \gamma \: \: \: than \: \\ evelute \: the \: value \: of \: \\ ( \alpha \beta + \beta \gamma + \gamma \alpha )$
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Answer 1

Answer:

$\alpha \beta + \beta \gamma + \gamma \alpha = \frac{c}{a}$

=》1/1

=》1

Answer 2

Given:-

p(x) = x³-6x²-x+30 = 0

where,

• a = 1
• b = -6
• c = -1
• d = 30

To find:-

αβ + βγ + γα

Formula:-

$\underline{\boxed{\sf αβ + βγ + γα = c/a}}$

Solution:-

αβ + βγ + γα = $\sf\dfrac{c}{a}$

αβ + βγ + γα = $\sf\dfrac{-1}{1}$ = -1

${\boxed {\sf αβ + βγ + γα = -1}}$