Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
208 views
in Polynomials by (71.6k points)
closed by
If `alpha` and `beta` are the zeroes of the polynomial `kx^2+4x+4`, such that `alpha^2+beta^2=24`. find the value of k.

1 Answer

0 votes
by (71.6k points)
selected by
 
Best answer
`alpha,beta`
`x^2+4x+3=0`
`alpha+beta=-4`
`alphabeta=3`
`1+beta/alpha+1+alpha/beta`
`2+(beta^2+alpha^2)/(alphabeta)`
`2+((alpha+beta)^2-2alphabeta)/(alphabeta)`
`2+(16-6)/3`
`16/3`
`(1+beta/alpha)(1+alpha/beta)`
`1+beta/alpha+alpha/beta+1`
`2+alpha/beta+beta/alpha`
`16/3`
`x^2`-(sum of roots)x+product of roots=0
`x^2-(1+alpha/beta+beta/alpha+1)+(1+alpha/beta)(1+beta/alpha)=0`
`x^22-16/3x+16/3=0`
`3x^2-16x+16=0`.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...