if L and B are the zeros of quadratic polynomial p(x)= ax square + bx +c then evaluate
Answers
Answer:
If α and β was of f(x)=ax
2
+bx+c. Then evaluate
aα+b
1
+
aβ+b
1
(aα+b)(aβ+b)
(aβ+b)+(aα+b)
=
a
2
αβ+abα+abβ+b
2
a(α+β)+2b
=
a
2
(αβ)+ab(α+β)+b
2
a(α+β)+2b
Using equation on the right side we get
=
a
2
(c/a)+ab(−b/a)+b
2
a(−b/a)+2b
=
ac−b
2
+b
2
−b+2b
=
ac
b
observe that, we have
α+β=
a
−b
αβ=
aIf α and β was of f(x)=ax
2
+bx+c. Then evaluate
aα+b
1
+
aβ+b
1
(aα+b)(aβ+b)
(aβ+b)+(aα+b)
=
a
2
αβ+abα+abβ+b
2
a(α+β)+2b
=
a
2
(αβ)+ab(α+β)+b
2
a(α+β)+2b
Using equation on the right side we get
=
a
2
(c/a)+ab(−b/a)+b
2
a(−b/a)+2b
=
ac−b
2
+b
2
−b+2b
=
ac
b
observe that, we have
α+β=
a
−b
αβ=
a
cIf α and β was of f(x)=ax
2
+bx+c. Then evaluate
aα+b
1
+
aβ+b
1
(aα+b)(aβ+b)
(aβ+b)+(aα+b)
=
a
2
αβ+abα+abβ+b
2
a(α+β)+2b
=
a
2
(αβ)+ab(α+β)+b
2
a(α+β)+2b
Using equation on the right side we get
=
a
2
(c/a)+ab(−b/a)+b
2
a(−b/a)+2b
=
ac−b
2
+b
2
−b+2b
=
ac
b
observe that, we have
α+β=
a
−b
αβ=
a
c