find the zeroes of x²_2x-8 and verify
the relationship between the zeroes and
co-efficient s.
Answers
Answer:
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Step-by-step explanation:
10th
Maths
Polynomials
Relationship between Zeroes and Coefficients of a Polynomial
Find the zeros of the quadr...
MATHS
Find the zeros of the quadratic polynomial f(x)=x
2
−2x−8 and verify the relationship between the zeros and their coefficients.
EASY
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ANSWER
f(x)=x
2
−2x−8
⇒f(x)=x
2
−4x+2x−8
⇒f(x)=x(x−4)+2(x−4)]
⇒f(x)=(x−4)(x+2)
Zeros of f(x) are given by f(x) = 0
⇒x
2
−2x−8=0
⇒(x−4)(x+2)=0
⇒x=4 or x=−2
So, α=4 and β=−2
∴ sum of zeros =α+β=4−2=2
Also, sum of zeros =
Coefficient of x
2
Coefficient of x
=
1
−(−2)
=2
So, sum of zeros =α+β=−
Coefficient ofx
2
Coefficient of x
Now, product of zeros =αβ=(4)(−2)=−8
Also, product of zeros =
Coefficient ofx
2
Constant term
=
1
−8
=−8
∴ Product of zeros =
Coefficient of x
2
Constant term
=αβ
Step-by-step explanation:
x^2 - 2x - 8 = 0
=> x^2 + 2x -4x - 8 = 0
x ( x + 2 ) -4 ( x + 2 ) = 0
( x + 2 ) ( x - 4 ) = 0
x = -2 or 4
The zeroes are 2 and -4.
Let,
alpha = -2
beta = 4
x^2 - 2x - 8 = 0
a = 1
b = -2
c = -8
The relationship between the zeroes and co-efficients,
alpha + beta = -b / a
-2 + 4 = - ( -2 ) / 1
2 = 2
alpha beta = c / a
- 2 ( 4 ) = - 8 / 1
- 8 = - 8
Hence, the relationship between the zeroes and co-efficients are verified.