If `a` is the root (having the least absolute value) or the equation `x^2-b x-1=0(b in R^+)` , then prove that `-1

If 2a+3b+6c=0, then prove that at least one root of the equation a x^2+b x+c=0 lies in the interval (0,1).

If the difference of the roots of the equation 2x^(2)-(a+1)x+a-1=0 is equal to their product then prove that a=2

Find the value of a if the equation 2x^2-(a+1)x+(a-1)=0 has equal roots.

The value of b for which the equation x^2+bx-1=0 and x^2+x+b=0 have one root in common is

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 s intheta,costheta be the roots of a x^2+b x+c=0 , then prove that b^2=a^2+2ac.

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

If the difference of the roots of the equation 2x^(2) - (a +1) x + a -1 = 0 is equal to their product, then prove that a = 2.

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