Question

please answer my question
solve both or do any 1

Answer 1

ans 2.
Given polynomial is -

p(x) = 6x3 + √2x2 - 10x - 4 √2

since x = √2 is a zero of p(x)

⇒ (x - √2) will be a factor of p(x)

divide the cubic polynomial by x-√2
the quotient will be
6x^2+7√2x+4
its middle term split will be
6x^2+4√2x+3√2x+4
2x(3x+2√2)+√2(3x+2√2)
(3x+2√2)=0 ; (2x-√2)=2
x=-2√2/3 ; x=-1/√2

Answer 2

9)Factoring x^3-6x^2+3x+10
Factors of 10 +1,-1,+2,-2,+5,-5,+10-10
Let f(x)=-1
-1-6-3+10=0
:.(x+1) is a factor.

Let f(x)=1
1-6+3+10=8

Let f(x)=-2
-8-24-6+10=-28

Let f(x)=2
8-24+6+10=0
:.(X-2) is a factor

Let f(x)=5
125-150+15+10=0
:.(X-5) is a factor.

:. Factors of x^3-6x^2+3x+10 are (x+1)(x-2)(x-5).

Now ATQ-
Factors are in the form A(A+B)(A+2B)

NOW EQUATION
A(A+B)(A+2B)=(X+1)(X-2)(X-5)
A=(X+1)...............(1)
(A+B)=(X-2).......(2)
(A+2B=(X-5)......(3)

PUTTING VALUE OF 1
(X+1)(X+1+B)(X+1+2B)=(X+1)(X-2)(X-5)
(X+1+B)(X+1+2B)=(X-2)(X-5)
:.(X+1+B)=(X-2).....1
(X+1+2B)=(X-5).....2
X-X+1+2=-B
3=-B
-3=B
:. (ANSWER)
B=-3
A=X
Factor=(X+1)(X-2)(X-5)

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Team Kancha