Question

pls answer this question​

Answer 1

Given,

f(x) = 2x³ + x²+bx-6

According to question,

if f(x) i.e 2x³ + x²+bx-6 is divided by x-3 then it leaves a reminder of 36.

so ,

2x³ + x² + bx - 6 - 36 will be divisible by x-3.

so that

(x-3) is an factor of 2x³ + x²+bx-42 = 0. ---------------------(i)

∴ x - 3 =0

x = 3

put the value of x in eqn(i).

2(3)³ + 3²+3b-42 = 0

⇒ 2*27 + 9 + 3b -42 =0

⇒ 54 + 9 -42 + 3b = 0

⇒ 21 = -3b

∴ b = - 21/3 = -7.

Now,

f(x) = 2x³ + x² - 7x - 6 -----------------------------(ii)

put x = 2;

f(x) = 2(2)³ + 2² - 7*2 - 6 = 16+4-14-6 = 0

so the one factor of the f(x) is x-2.

Divide the eqn(ii) by (x-2) to find out remaining two factors.

x-2) 2x³ + x² - 7x - 6 (2x² + 5x +3

-(2x³ - 4x²)

------------------------

0 + 5x² - 7x - 6

- (5x² - 10x)

----------------------

0 + 3x - 6

- (3x - 6)

------------------

0 + 0

Hence another factor will be 2x² + 5x +3 but, it's in a quadratic form so solve this quadratic equation to get the factors.

2x² + 5x + 3 = 0

⇒ 2x² + 3x + 2x +3 = 0

⇒ x(2x +3) +1(2x + 3) = 0

⇒ (x + 1)(2x + 3) = 0

|

x + 1 = 0 | 2x + 3 = 0

x = - 1 | 2x = -3

| x = -3/2

Therefore the factors are 2, -1 & -3/2

And, Value of b = -7


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Answer 2

hope you will understand ...............