Question

❤❤chapter no. 2❣❣❣❣❣
❤❤ex. 2.4 ❣❣❣❣❣
❤❤question no. 4❣❣❣❣❣ ♢
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♧❤❤❤thanks### ❤❤❤♧
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Answer 1

Answer:

hope it helps you

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Step-by-step explanation:

ANSWER

Given:-

→ p(x)= x³ -3x² +x+1

and the zeroes are

→ (a-b), a ,(a+b)

\alpha \: + \beta \: + \gamma = \frac{ - b}{a}α+β+γ=

a

−b

Here ,

→ a = 1

→ b = -3

→ c = 1

→ d = 1

→ a - b + a + a + b = -(-3)/1

→ 3a = 3

→ a = 3/3

→ a = 1.

Now,

\alpha \times \beta \times y = \frac{ - d}{a}α×β×y=

a

−d

→ (a - b) (a) (a+b) = -d/a

→ (a-b) (a+b) (a)= -1/1

→ a² - b² × a = -1

put the value of a in it

→ 1² - b² ×1 = -1

→ 1 - b² = -1

→ -b² = -1-1

→ -b² = -2

→ b = ±√2

Answer 2

The other zeroes are -5 and 7.

Step-by-step explanation:

You must know the introduction that,

Introduction :

Try factorizing the number 8,

$\bigstar\;\begin{array}{r | l}2 & 8\\\cline{2-2} 4 & 4\\\cline{2-2} & 1\end{array}$

2 is the factor of 8.

4 is the factor of 8.

So,

⇒ 2 × 4

⇒ 8

2 × 4  is the factor of 8.

Note :

I used number "4" but "2" can also be used. I used "4" because it will give better explanation in this method.

We will use same in our question.

Solution :

Given :

The polynomial :

$\bf p(x)=x^4-6x^3-26x^2+138x-35$

$\bf 2\pm \sqrt{3}$ are two zeroes.

To Find :

The other zeroes.

• Method :

As given,

$\bf 2\pm \sqrt{3}$ are two zeroes.

So,

Th factors of given polynomial,

$\bf(x-2+\sqrt{3})\text{ and }(x-2-\sqrt{3})$

$\implies \sf (x-2+\sqrt{3})(x-2-\sqrt{3})\\ \\ \\\implies \sf (x-2)^2-3\\ \\ \\\implies \sf x^2-4x+4-3\\ \\ \\\implies \sf x^2-4x+1$

Now,

We have to find the remaining factors. So, we will divide the given polynomial by x² - 4x + 1

Using long division method, We get :

$\implies \sf \dfrac{x^4-6x^3-26x^2+138x-35}{x^2-4x+1}=x^2-2x-35$

We have to find the other zeroes now, We have to equate the remaining factors equal to zero.

So,

$\implies \sf x^2-2x-35=0\\ \\ \\\implies \sf x^2-7x+5x-35=0\\ \\ \\\implies \sf x(x-7)+5(x-7)=0\\ \\ \\\implies \sf (x-7)(x+5)=0$

Now, Each factor is equal to 0.

• x = 7
• x = - 5

Hence,

The other zeroes are -5 and 7.