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, the equation 3ax^(2)+2bx+c=0 has , 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 Rdot

If a , b , c , are real number such that a c!=0, then show that at least one of the equations a x^2+b x+c=0 and -a x^2+b x+c=0 has real roots.

If exactly one root of the quadratic equation x ^(2) -(a+1 )x +2a =0 lies in the interval (0,3) then the set of value 'a' is given by :

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

If a lt c lt b then the roots of the equation (a−b)x^2 +2(a+b−2c)x+1=0 are

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.

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.

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

If alpha is the root (having the least absolute value) of the equation x^2-b x-1=0(b in R^+) , then prove that -1ltalphalt0.