wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If αand βare the roots of the quadratic equationx2+px+q=0, then the values of α3+β3 and α4+α2β2+β4 are respectively


A

3pqp3and p43p2q+3q2

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

-p(3qp2)and (p2q)(p2+3q)

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

pq4and p4q4

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

3pqp3 and (p2q)(p23q)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

3pqp3 and (p2q)(p23q)


Explanation for correct option:

Find the values of α3+β3 and α4+α2β2+β4:

Given that If αand βare the roots of the quadratic equationx2+px+q=0

(α+β)=-p;αβ=q

Now, α3+β3=(ɑ+β)33ɑβ[ɑ+β]

=(-p)33q(-p)=p3+3pq

α3+β3=-p3+3pq

And α4+α2β2+β4=(α2+β2)2(ɑβ)2

=[(ɑ+β)22ɑβ]2(ɑβ)2=[(-p)22q]2q2=(p22q)2q2=p4+4q24p2qq2=p4+3q24p2q=(p2q)(p23q)

α4+α2β2+β4=(p2q)(p2-3q)

Hence, the correct option is (D).


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Algebraic Operations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon