Question

4. If a + b + c = 9 and a² + b +c²= 35, Find the value of a3+ b3 + c3- 3abc.
5. Factorise:-
10√2 x² + 3x - 9√2
6. Find the remainder when f(x) = x3 - 6x²+ 2x - 4 is divided by g(x) = 3x-1
7. Find the value of a such that x - 4 is a factor of 5x3 - 7x² - ax- 28.
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Answer 1

Answer:

4 . If a + b + c = 9 and a² + b² +c²= 35, Find the value of a3+ b3 + c3- 3abc.

Ans = 108

a2+b2+c2=(a+b+c)2-2(ab+bc+ca)

35=81-2(ab+bc+ca)

2(ab+bc+ca)=46.

(ab+bc+ca)=23

a3+b3+c3-3abc

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

substituting values,

a3+b3+c3-3abc=9×(35-23)=9×12=108.

5 . Factorise:-  10√2 x² + 3x - 9√2

Ans :

$= 5.1\sqrt{2}x^2+3x-9\sqrt{2}\\= 7.21248\dots x^2+3x-12.72792\dots$

6 . Find the remainder when f(x) = x3 - 6x²+ 2x - 4 is divided by g(x) = 3x-1

Ans :

1 - 2x = 0

- 2x = - 1

2x = 1

x = 1/2

p(x) = x³ - 6x² + 2x - 4

p(1/2) = (1/2)³ - 6*(1/2)² + 2*(1/2) - 4

= 1/8 - 6*(1/4) + 1 - 4

= 1/8 - 6/4 + 1 - 4  

= 1/8 - 3/2 + 1 - 4

Taking L.C.M. of the denominators and then solving it.

= (1 - 12 + 8 - 32)/8

= - 35/8

Remainder is - 35/8

7 .  Find the value of a such that x - 4 is a factor of 5x3 - 7x² - ax- 28.

Ans : Image attached