Consider the equation (x 2 +x+1) 2 -(m-3)(x 2 +x+1

Question

Consider the equation (x2+x+1)2-(m-3)(x2+x+1) +m=0. Where m is a real parameter. The number of positive integral value of m for which two distinct real roots is??? Also The number of positive integral values of m ,mfour distinct real roots is????

Satyajit Samal · Accepted Answer

Suppose x^2+x+1 = tSo, the equation can be written as t^2 – (m-3)t + m = 0 This equation will have two distinct real roots if (m-3)^2 > 4mm^2 -10m + 9 > 0 (m-1)(m-9) > 0 m 9 …....(i) Now t = x^2 + x + 1 = (x + 1/2)2+ 3/ 4Part -1: So if t > 3/ 4 , then x2+ x + 1 = t will have two distinct roots, hence the original equation will have four distinct roots.For the equation t2 - (m-3)t + m = 0 , if t > 3/ 4, then f (3/ 4) > 0 9/ 16 – (m-3) 3/ 4 + m > 0 m > -45/4 …......... (ii)Also (m-3)/ 2 > 3/ 4 ( -b / 2a of quadratic is > 3/ 4)m > 9/2 …............ (iii)So, M should satisfy the conditions in (i), (ii) and (iii). Combining, all the positive integers > 9 ( 10, 11, 12, 13....) as values of m will give four distinct roots for the given equation. Part-2: For two real roots, both roots of equation t2 - (m-3)t + m = 0 should be on different side of 3/ 4 , that is one greater than 3/ 4 , and the other one less than 3/ 4.So, f (3/ 4) m Since we need positive integral values of m, no value for m possible in this case.

Algebra> Consider the equation (x 2 +x+1) 2 -(m-3)...

Consider the equation (x²+x+1)²-(m-3)(x²+x+1) +m=0. Where m is a real parameter. The number of positive integral value of m for which two distinct real roots is??? Also The number of positive integral values of m ,m
four distinct real roots is????

Mostafijur Rahaman , 11 Years ago

Satyajit Samal

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> Consider the equation (x 2 +x+1) 2 -(m-3)...

Consider the equation (x2+x+1)2-(m-3)(x2+x+1) +m=0. Where m is a real parameter. The number of positive integral value of m for which two distinct real roots is??? Also The number of positive integral values of m ,mfour distinct real roots is????

Mostafijur Rahaman , 11 Years ago

Satyajit Samal

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

Consider the equation (x²+x+1)²-(m-3)(x²+x+1) +m=0. Where m is a real parameter. The number of positive integral value of m for which two distinct real roots is??? Also The number of positive integral values of m ,m
four distinct real roots is????