Let a, b and c be real numbers such that `4a + 2b + c = 0` and `ab gt 0.` Then the equation ax^(2) + bx + c = 0` has

Let a ,b ,and c be real numbers such that 4a+2b+c=0 and a b > 0. Then the equation a x^2+b x+c = 0

If a + b + c = 0 then the quadratic equation 3ax^(2) + 2bx + c = 0 has

If a, b, c, d are real numbers such that (3a + 2b)/(c+d)+3/2=0 then the equation ax^3 + bx^2 + cx + d =0 has

Let a,b,c be real numbers in G.P. such that a and c are positive , then the roots of the equation ax^(2) +bx+c=0

Let a,b,c in R and a ne 0 be such that (a + c)^(2) lt b^(2) ,then the quadratic equation ax^(2) + bx +c =0 has

Let a gt 0, b gt 0 and c lt0. Then, both the roots of the equation ax^(2) +bx+c=0

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 a,b, c epsilon R(a!=0) and a+2b+4c=0 then equatio ax^(2)+bx+c=0 has

If a , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then

If a, b, c, d are real numbers such that (a+2c)/(b+3d)+(4)/(3)=0 . Prove that the equation ax^(3)+bx^(2)+cx+d=0 has atleast one real root in (0, 1).