5
6. Find the quadratic polynomial, the sum of whose zeros is and their
2
product is 1. Hence, find the zeros of the polynomial.
7. Find the quadratic polynomial whose zeros are 2 and 6. Verify the
relation between the coefficients and the zeros of the polynomial.
Lid
Answers
Step-by-step explanation:
6).
Given that
The sum of zeroes = 2
Product of zeroes = 1
We know that
α and β are the zeores then the quadratic polynomial is K[x^2-(α + β )x +α β ]
we have α + β = 2 and αβ = 1
The Polynomial = K[x^2-(2x)+1]
=>K(x^2-2x+1)]
If K = 1 then the required Polynomial = x^2-2x+1
Answer:-
The quadratic Pilynomial is x^2-2x+1
_______________________________
7).
Given that
Zeroes of a quadratic polynomial are 6 and 2
Let α = 6
Let β = 2
We know that
α and β are the zeores then the quadratic polynomial is K[x^2-(α + β )x +α β ]
=>K[x^2-(6+2)+(6×2)]
=>K[x^2-8x+12]
If K = 1 then the required Polynomial is x^2-8x+12
Relationship between the zeroes and the coefficients:-
Now, on comparing with the standard quadratic polynomial ax^2+bx+c
a = 1
b= -8
c=12
α = 6
β = 2
Sum of the zeores = α+ β = 6+2 = 8
Sum of the zeroes = -b/a = -(-8)/1=8
Product of zeroes = 6×2 = 12
Product of the zeroes = c/a = 12/1=12
Verified the given relations.
______________________________
Used formulae:-
- α and β are the zeores then the quadratic polynomial is
- K[x^2-(α + β )x +α β ]
- Sum of the zeroes = -b/a
- Product of the zeroes = c/a
Answer:
6 - k(x^2 - 2x + 1)
here k≠0
7 - x^2 - 8x + 12
Step-by-step explanation:
- we know
quadratic polynomial = x^2 - (sum of zeroes)x + product of zeroes
so,
sum = 2+6 = 8
product = 6×2 =12
quadratic polynomial= x^2 - 8x + 12
= x^2 - 6x - 2x + 12
= x ( x - 6 ) - 2 ( x - 6 )
= ( x - 2 ) ( x - 6 )
= x = 2 x = 6
sum = 2+6 = -b/a
8 = -(-8/1)
8 = 8
Product = 6×2 = c/a
12 = 12/1
12 = 12
Hope it helps