Ifαandβaretherootsofx2+7x+10=0findthevaluesofi)α2
β
+β2
α
ii)α2+β
Answers
Answer:
ANSWER
Given: f(x)=3x
2
−7x−6
Which is of the from ax
2
+bx+c
⇒a=3,b=−7,c=−6
Now, α+β=−
a
b
=
3
−(−7)
α+β=
3
7
....(1)
and αβ=
a
c
=
3
−6
αβ=−2...(2)
(1) α
2
+β
2
=(α+β)
2
−2α+β
=(
3
7
)
2
−2(−2) [ from (1) & (2)]$$
=
9
49
+4=
9
49+36
=
9
85
α
2
β
2
=(αβ)
2
=(−2)
2
=4
The pohynomical whose roots are α
2
,β
2
is given by , x
2
−(sumofroots)x+productofroots
=x
2
−
9
85x
+4
=
9
9x
2
−85x+36
=
9
1
(9x
2
−85x+36)
(2) (2α+3β)+(3α+2β)=5α+5β
=5(α+β)
=5⋅
3
7
=
3
35
(2α+3β)+(3α+2β)=6α
2
4αβ+9αβ+6β
2
=6(α
2
+β
2
)+13αβ
=6{(α+β)
2
−2αβ}+Bαβ
=6(α+β)
2
−12αβ+Bαβ
=6(α+β)
2
+αβ
=6(
3
7
)
2
+(−2)
=6⋅
9
49
−2
=
3
98
−2
=
3
98−6
=
3
92
the required polynomial whose you are (2α+3β) and (3α+2β) is
x
2
−
3
35
x+
3
92
=
3
1
(3x
2
−35x+92)
Answered By
toppr
1066 Views
How satisfied are you with the answer?
This will help us to improve better
answr
Get Instant Solutions, 24x7
No Signup required
girl
Related Questions to study
Let P(x) is polynomial of degree n, having n real and distinct non zero roots. Q(x) is another polynomial of degree m such that Q
′
(x)=0 has at least one real root not equal to any of the root of P(x)=0. If n, m >2 then which of the following statements is correct
(I): x
2
P
′′
(x)+3xP
′
(x)+P(x)=0 has n real roots
(II): P
′
(x)Q
′
(x)+P(x)Q
′′
(x)=0 has at least one real root.
Study later
View Answer
Divide:q
2
−4q−32 by q+4
Study later
View Answer
VIEW MORE
Create custom Assignments
Customize assignments and download PDF’s
girl
BROWSE BY
ClassesBoardsExams
MODULES
Online ClassesMock TestsAdaptive PracticeLive Doubts
Stay upto date with our Newsletter!
Stay informed, stay ahead. Be a topper
Your email address
About Us
Brand Resources
Press
Customer Stories
Jobs
Educators
Fellowship
Learning Planet
Guides
Ask
Blog
Bytes
News
Terms of Service
Privacy Policy
Contact Us
FAQs
Google Play
App Store
IN
India