Question

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Answer 1

Answer :

8.

Given that,

a + b + c = 15

or, (a + b + c)² = 15²

or, (a² + b² + c²) + 2 (ab + bc + ca) = 225

or, 83 + 2 (ab + bc + ca) = 225,

given that a² + b² + c² = 83

or, 2 (ab + bc + ca) = 225 - 83 = 142

or, ab + bc + ca = 71

∴ a³ + b³ + c³ - 3abc

= (a + b + c) {a² + b² + c² - (ab + bc + ca)}

= 15 (83 - 71)

= 15 × 12

= 180

9.

The given polynomial is

f (x) = 2x² + kx

Since, (x + 1) is a factor of f (x),

f (- 1) = 0

or, 2 (- 1)² + k (- 1) = 0

or, 2 - k = 0

i.e., k = 2

10.

Now,

(x + y)³ - (x³ + y³)

= x³ + 3x²y + 3xy² + y³ - x³ - y³

= 3x²y + 3xy²

= 3xy (x + y)

11.

Given that,

p (x) = x² - 4x + 5

Now, p (- 1) + p (0) - p (1)

= {(- 1)² - 4 (- 1) + 5} + {0² - 4 (0) + 5} - {1² - 4 (1) + 5}

= (1 + 4 + 5) + (5) - (1 - 4 + 5)

= 10 + 5 - 2

= 13

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