If `alphaa n dbeta` are roots of the quadratic equation `a x^2+b x+c=0` and `a+b+c >0,a-b+c >0&c<0,t h e n[alpha]+[beta]` is equal to (where `[dot]` denotes the greatest integer function) (a)`10` (b) `-3` (c) `-1` (d) `0`

If alpha is a real root of the quadratic equation a x^2+b x+c=0a n dbeta ils a real root of - a x^2+b x+c=0, then show that there is a root gamma of equation (a//2)x^2+b x+c=0 whilch lies between aa n dbetadot

Let alpha,beta be the roots of the quadratic equation a x^2+b x+c=0 and delta=b^2-4a cdot If alpha+beta,alpha^2+beta^2alpha^3+beta^3 are in G.P. Then a. =0 b. !=0 c. b =0 d. c =0

The roots of the quadratic equation (a + b-2c)x^2+ (2a-b-c) x + (a-2b + c) = 0 are

If alphaa n dbeta are the roots of the equation x^2+b x+c=0 ,where c 0 b c then (a) 0 α 0 β 2 α 2 alpha (c) α α 0 α 2 β 2 alpha

If alphaa n dbeta are roots of the equation a x^2+b x+c=0, then the roots of the equation a(2x+1)^2-b(2x+1)(3-x)+c(3-x)^2=0 are (2alpha+1)/(alpha-3),(2beta+1)/(beta-3) b. (3alpha+1)/(alpha-2),(3beta+1)/(beta-2) c. (2alpha-1)/(alpha-2),(2beta+1)/(beta-2) d. none of these

Let alpha,beta be the roots of the quadratic equation ax^2+bx+c=0 then the roots of the equation a(x+1)^2+b(x+1)(x-2)+c(x-2)^2=0 are:-

If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of the equations a x^2+2b x+c=0,2b x^2+c x+a=0a d nc x^2+a x+2b=0, respectively, where a, b, and c are positive real numbers, then alpha+alpha^2= a. a b c b. a+2b+c c. -1 d. 0

Write the roots of the equation (a-b)x^2+(b-c)x+(c-a)=0.

If alphaa n dbeta are the zeros of the quadratic polynomial f(x)=a x^2+b x+c , then evaluate: alpha^4beta^4

Let a,b,c,d be distinct real numbers and a and b are the roots of the quadratic equation x^2-2cx-5d=0 . If c and d are the roots of the quadratic equation x^2-2ax-5b=0 then find the numerical value of a+b+c+d .