if a, b, y are the zeroes of a cubic polynomial ax^3+bx^2+cx+d, then a+b+y=?
Answers
Answer:
-d /a
Step-by-step explanation:
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10th
Maths
Polynomials
Relationship between Zeroes and Coefficients of a Polynomial
If alpha, beta, gamma are t...
MATHS
If α,β,γ are the zeroes of a cubic polynomial ax
3
+bx
2
+cx+d, then the product of zeroes is
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ANSWER
Ggiven that
p(x)=ax
3
+bx
2
+cx+d .........(1) where a
=0 is a cubic polynomial
And α,β,γ are the zeroes of the polynomial p(x)
We can also write the polynomial in this way
p(x)=(x−α)(x−β)(x−γ)
⇒p(x)=x
3
−(α+β+γ)x
2
+(αβ+βγ+γα)x−αβγ .............(2)
Equations (1) and (2) are same
Comparing the coefficients
1
a
=
−α−β−γ
b
=
αβ+βγ+γα
c
=
−αβγ
d
On solving we get the following results
α+β+γ=
a
−b
= Sum of the roots
αβ+βγ+γα=
a
c
αβγ=
a
−d
= product of roots