Question

16. If (x+a) (x+b) (x+c) = x3 - 10x2 + 45 x - 15, then find the value of a2+ b2 + c2​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

10

Step-by-step explanation:

In a cubic polynomial of the form,

$\alpha {x}^{3} + \beta {x}^{2} + \gamma x + d = 0$

$sum \: of \: roots \: ofa \: cubic \: polynomial = \frac{ - \beta }{a} = \frac{ - ( - 10)}{1} = 10$

$sum \: of \: roots \: ofa \: cubic \: polynomial \: taken \: two \: at \: a \: time = \frac{ \gamma }{a} = \frac{ 45}{1} = 45$

Now,

$a + b + c = 10$

$ab + bc + ca = 45$

So,

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca)$

Solving bu putting values into this, we get

{a}^{2} + {b}^{2} + {c}^{2} = 10