If equation x^4+px^3+qx^2+rx+5=0 has four real roo

Question

If equation x^4+px^3+qx^2+rx+5=0 has four real roots then find the minimum value of p.r

Arun Kumar · Accepted Answer

Hello Studentpr=20+k \\=>k=12*5( {\sum {r_i \over r_j}}) \\=>({\sum {r_i \over r_j}}) \geq \sqrt{\prod {{\sum {r_i \over r_j}}}}=1 \\=> total sum \geq 80 \\ src=http://latex.codecogs.com/gif.latex?%5C%5C%20%5C%5C%20%5Csum%20r_i%3D-p%20%5C%5C%20%5Csum%20r_i.r_j%3Dq%20%5C%5C%20%5Csum%20r_i.r_jr_k%3D-r%20%5C%5C%20r_i.r_jr_k.r_l%3D5%20%5C%5Cpr%3D%5Csum%20r_i%20*%20%5Csum%20r_i.r_jr_k%3D20&plus;%20%5C%5C%243%20terms%20of%20%24r_i%5E2*%24product%20of%20other%20any%20two%24%20%5C%5C&plus;%243%20terms%20of%20%24r_j%5E2%24product%20of%20other%20any%20two%24%20%5C%5C&plus;%243%20terms%20of%20%24r_k%5E2%24product%20of%20other%20any%20two%24%20%5C%5C&plus;%243%20terms%20of%20%24r_l%5E2%24product%20of%20other%20any%20two%24%20%5C%5Cr_i%5E2r_jr_k%3D%7B%20r_i*r_i.r_jr_k.r_l%20%5Cover%20r_l%7D%3D%7B5%20r_i%20%5Cover%20r_j%7D%20%5C%5C%3D%3Epr%3D20&plus;k%20%5C%5C%3D%3Ek%3D12*5%28%20%7B%5Csum%20%7Br_i%20%5Cover%20r_j%7D%7D%29%20%5C%5C%3D%3E%28%7B%5Csum%20%7Br_i%20%5Cover%20r_j%7D%7D%29%20%5Cgeq%20%5Csqrt%7B%5Cprod%20%7B%7B%5Csum%20%7Br_i%20%5Cover%20r_j%7D%7D%7D%7D%3D1%20%5C%5C%3D%3E%20total%20sum%20%5Cgeq%2080%20%5C%5C>Thanks & RegardsArun KumarBtech, IIT DelhiAskiitians Faculty

Algebra> If equation x^4+px^3+qx^2+rx+5=0 has four...

If equation x^4+px^3+qx^2+rx+5=0 has four real roots then find the minimum value of p.r

Arushi Singh , 11 Years ago

Arun Kumar

LIVE ONLINE CLASSES

What is a binomial expression?

algebra

Can we divide two vectors? If this is possible then how?

algebra

How do you write “the product of 18 and q” as an algebraic expression?

algebra

दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे

algebra

Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?

algebra

Algebra> If equation x^4+px^3+qx^2+rx+5=0 has four...

If equation x^4+px^3+qx^2+rx+5=0 has four real roots then find the minimum value of p.r

Arushi Singh , 11 Years ago

Arun Kumar

LIVE ONLINE CLASSES

Other Related Questions on algebra

What is a binomial expression?

algebra

Can we divide two vectors? If this is possible then how?

algebra

How do you write “the product of 18 and q” as an algebraic expression?

algebra

दहावीच्या आय सी एस इ विद्यार्थ्यांनी पुढे काय करायला पाहिजे

algebra

Find the least number of square tiles by which the floor of a room of dimensions 16.58 m and 8.32 m can be covered completely. why HCF and not LCM as “least” keywor dis given?

algebra