If `a ,b ,c in R^+a n d2b=a+c ,` then check the nature of roots of equation `a x^2+2b x+c=0.`

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0 where a ,b ,c in R

if a lt c lt b, then check the nature of roots of the equation (a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0

If a+b+c=0 then check the nature of roots of the equation 4a x^2+3b x+2c=0w h e r ea ,b ,c in Rdot

If a ,b ,c in R , then find the number of real roots of the equation =|x c-b-c x a b-a x|=0

If a ,b ,c in R , then find the number of real roots of the equation Delta =|[x, c,-b],[-c, x, a], [b,-a,x]|=0

Let a ,b ,c be real numbers with a!=0a n dl e talpha,beta be the roots of the equation a x^2+b x+c=0. Express the roots of a^3x^2+a b c x+c^3=0 in terms of alpha,betadot

If a ,b ,c are non zero rational no then prove roots of equation (a b c^2)x^2+3a^2c x+b^2c x-6a^2-a b+2b^2=0 are rational.

If a ,b ,c in R such that a+b+c=0a n da!=c , then prove that the roots of (b+c-a)x^2+(c+a-b)x+(a+b-c)=0 are real and distinct.

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 alpha & beta

If alpha,beta are the roots of the equation a x^2+b x+c=0, then find the roots of the equation a x^2-b x(x-1)+c(x-1)^2=0 in term of alphaa n dbetadot