If 1,-1 and 2 are zeroes of a polynomial p(x)=x3- ax2 -bx+2 find the v

1.	If 1,-1 and 2 are zeroes of a polynomial p(x)=x3- ax2 -bx+2 find the values of a and bplz answer this question as soon as possible this is important who will give answer correctly I will follow them give thanks mark as brainliest and rate youunsual answers will be reported plz do it fast
Answer» Answer : a = 2, b = 1 Step-by-step EXPLANATION : Can be solved in TWO ways, substituting the values of zeroes in place of X from the relationship between zeroes and coefficients _______________________ Method - 1 : Given polynomial, p(x) = x³ - ax² - bx + 2 >>> 1,-1 and 2 are zeroes of a polynomial So, when we substitute the above values in place of x ; the result is zero. Put x = 1, p(1) = 0 1³ - a(1)² - b(1) + 2 = 0 1 - a - b + 2 = 0 3 - a - b = 0 $\boxed{\bf a+b=3}$ Put x = -1, p(-1) = 0 (-1)³ - a(-1)² - b(-1) + 2 = 0 -1 - a(1) + b + 2 = 0 -1 - a + b + 2 = 0 - a + b + 1 = 0 $\boxed{\bf b-a=-1}$ Put x = 2, p(2) = 0 2³ - a(2)² - b(2) + 2 = 0 8 - a(4) - 2b + 2 = 0 8 - 4a - 2b + 2 = 0 4a + 2b = 10 2(2a+b) = 2(5) $\boxed{\bf 2a+b=5}$ ______________________ We got three EQUATIONS, a + b = 3 --(1) b - a = -1 --(2) 2a + b = 5 --(3) Equation (1) a + b = 3 a = 3 - b substitute the value of a in equation (2) Equation (2) b - a = -1 b - (3-b) = -1 b - 3 + b = -1 2b = 3 - 1 2b = 2 b = 2/2 b = 1 => a = 3 - b = 3 - 1 = 2 Substitute the values of a and b in equation (3) to VERIFY >> 2a + b 2(2) + 1 4 + 1 5 Therefore, a = 2, b = 1 ____________________ Method - 2 : For a cubic polynomial of the form, ax³ + bx² + cx + d Let α,β,γ are the zeroes RELATIONSHIP BETWEEN ZEROES AND COEFFICIENTS : ➤ α + β + γ = -b/a ➤ αβ + βγ + αγ = c/a ➤ αβγ = -d/a Given polynomial, x³ - ax² - bx + 2 and its zeroes : 1,-1,2 From the above relation, => 1 + (-1) + 2 = -(-a)/1 1 - 1 + 2 = a a = 2 => (1)(-1) + (-1)(2) + (2)(1) = -b/1 -1 - 2 + 2 = -b -b = -1 b = 1 ∴ a = 2, b = 1

If 1,-1 and 2 are zeroes of a polynomial p(x)=x3- ax2 -bx+2 find the values of a and bplz answer this question as soon as possible this is important who will give answer correctly I will follow them give thanks mark as brainliest and rate youunsual answers will be reported plz do it fast

Answer»

Answer :

a = 2, b = 1

Step-by-step EXPLANATION :

Can be solved in TWO ways,

substituting the values of zeroes in place of X
from the relationship between zeroes and coefficients

_______________________

Method - 1 :

Given polynomial,

p(x) = x³ - ax² - bx + 2

>>> 1,-1 and 2 are zeroes of a polynomial

So, when we substitute the above values in place of x ; the result is zero.

Put x = 1,

p(1) = 0

1³ - a(1)² - b(1) + 2 = 0

1 - a - b + 2 = 0

3 - a - b = 0

$\boxed{\bf a+b=3}$

Put x = -1,

p(-1) = 0

(-1)³ - a(-1)² - b(-1) + 2 = 0

-1 - a(1) + b + 2 = 0

-1 - a + b + 2 = 0

- a + b + 1 = 0

$\boxed{\bf b-a=-1}$

Put x = 2,

p(2) = 0

2³ - a(2)² - b(2) + 2 = 0

8 - a(4) - 2b + 2 = 0

8 - 4a - 2b + 2 = 0

4a + 2b = 10

2(2a+b) = 2(5)

$\boxed{\bf 2a+b=5}$

______________________

We got three EQUATIONS,

a + b = 3 --(1)

b - a = -1 --(2)

2a + b = 5 --(3)

Equation (1)

a + b = 3

a = 3 - b

substitute the value of a in equation (2)

Equation (2)

b - a = -1

b - (3-b) = -1

b - 3 + b = -1

2b = 3 - 1

2b = 2

b = 2/2

b = 1

=> a = 3 - b

= 3 - 1

= 2

Substitute the values of a and b in equation (3) to VERIFY

>> 2a + b

2(2) + 1

4 + 1

Therefore, a = 2, b = 1

____________________

Method - 2 :

For a cubic polynomial of the form,

ax³ + bx² + cx + d

Let α,β,γ are the zeroes

RELATIONSHIP BETWEEN ZEROES AND COEFFICIENTS :

➤ α + β + γ = -b/a

➤ αβ + βγ + αγ = c/a

➤ αβγ = -d/a

Given polynomial,

x³ - ax² - bx + 2

and its zeroes : 1,-1,2

From the above relation,

=> 1 + (-1) + 2 = -(-a)/1

1 - 1 + 2 = a

a = 2

=> (1)(-1) + (-1)(2) + (2)(1) = -b/1

-1 - 2 + 2 = -b

-b = -1

b = 1

∴ a = 2, b = 1