Find the quadratic polynomial, sum of whose zeroes is 25 and their product is 1. Hence find the zeroes of the polynomial.

Given :-α+β= 52αβ=1P(x)=x2−(α+β)x+αβP(x)=x2−25x+1=2x2−5x+2P(x)=02x2−5x+2=02x2−4x−x+2=02x(x−2)−1(x−2)=0(2x−1)(x−2)=02x−1=0 & x−2=0x= 12 & x=2 are zeros of P(x)

Get 2 FREE Instant-Explanations on Filo with code FILOAPP

Home

Find the quadratic polynomial, sum of whose zeroes is 52 and t

Question

Find the quadratic polynomial, sum of whose zeroes is $\frac{5}{2}$ and their product is $1.$ Hence find the zeroes of the polynomial.

Views: 703 students

Found 2 tutors discussing this question

Evelyn Discussed

Find the quadratic polynomial, sum of whose zeroes is

\frac{5}{2}

and their product is

1.

Hence find the zeroes of the polynomial.

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

Given :-

α + β = 52

α β = 1

P (x) = x^{2} - (α + β) x + α β

P (x) = x^{2} - \frac{5}{2} x + 1

= 2 x^{2} - 5 x + 2

P (x) = 0

2 x^{2} - 5 x + 2 = 0

2 x^{2} - 4 x - x + 2 = 0

2 x (x - 2) - 1 (x - 2) = 0

(2 x - 1) (x - 2) = 0

2 x - 1 = 0

x - 2 = 0

x = 12

x = 2

are zeros of P(x)

Was this solution helpful?

150

Report

One destination for complete JEE/NEET preparation

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our math tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	Find the quadratic polynomial, sum of whose zeroes is $\frac{5}{2}$ and their product is $1.$ Hence find the zeroes of the polynomial.
Answer Type	Text solution:1
Upvotes	150

Find the quadratic polynomial, sum of whose zeroes is 25​ and their product is 1. Hence find the zeroes of the polynomial.

Text solutionVerified

Practice questions from similar books

Find the quadratic polynomial, sum of whose zeroes is $\frac{5}{2}$ and their product is $1.$ Hence find the zeroes of the polynomial.