Q 1) find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficient 1) x²-2x-8.
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7
Answer:
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
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Answer:
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Step-by-step explanation:
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