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If the zeros of the polynomial ax²+bx+b=0 are in the ratio m:n then find the value of √(m/n)+√(n/m).

Posted by Vaishnavi Saha 5 years, 4 months ago

CBSE > Class 10 > Mathematics

2 answers

Vaishnavi Saha 5 years, 4 months ago

Let α and β are two zeroes of the polynomial ax²+bx+b. Sum of zeroes = -(b)/a = α+β Product of zeroes = c/a = αβ = b/a α/β = m/n Now, √m/n + √n/m =√α/β + √β/α =√α/√β + √β/√α =(α+β)/√αβ =(-b/a)/√b/a =-√b/√a

Gaurav Seth 5 years, 4 months ago

Question : If the zeros of the polynomial ax²+bx+b=0 are in the ratio m:n then find the value of √(m/n)+√(n/m) .

Answer :

OR

let the zeros of the given polynomial ax^2+bx+c be m"alpha" and n"alpha"

m "alpha " + n"alpha" = -b/a

=>"alpha"= -b/a(m+n)------------------(i)

and similarly product of zeros

=> mn"alpha^2"=b/a-------------(ii)

Now,

Putting the value of equation (i) in equation (ii)

You would get the desired answer which is

root m/ root n +root n/root m

=>root b/a

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