If `altbltcltd ,`="" then="" the="" roots="" of="" equation="" `(x-a)(x-c)+2(x-b)(x-d)="0`" are="" real="" and="" distinct.="" (1984,="" 1m)

True or false The equation 2x^2+3x+1=0 has an irrational root. If a

If altbltcltd then show that the quadratic equation mu(x-a)(x-c)+lamda(x-b)(x-d)=0 has real roots for all real mu and lamda

If a,b and c are real numbers then the roots of the equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are always

If a

If a lt b lt c lt d then show that (x-a)(x-c)+3(x-b)(x-d)=0 has real and distinct roots.

If a,b,c,d are four consecutive terms of an increasing A.P.then the roots of the equation (x-a)(x-c)+2(x-b)(x-d)=0 are a. non-real complex b.real and equal c.integers d.real and distinct

If (a+b+c)>0 and a < 0 < b < c, then the equation a(x-b)(x-c)+b(x-c)(x-a)+c(x-a)(x-c)=0 has (i) roots are real and distinct (ii) roots are imaginary (iii) product of roots are negative (iv) product of roots are positive