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 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+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 and c are in A.P. and one root of the equation a x^2+b c+c=0 is 2 , the find the other root dot

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.

Prove that the roots of the equation (a^4+b^4)x^2+4a b c dx+(c^4+d^4)=0 cannot be different, if real.

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 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 show that the equation a x^2 + bx + c = 0 has atleast one real root between 0 to 1.

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot

If a and b are the real roots of the equation x^(2) - kx + c = 0, then the distance between the points (a, 0) and (b, 0) is