If the equation `x^2=a x+b=0` has distinct real roots and `x^2+a|x|+b=0` has only one real root, then which of the following is true? `b=0, a >0` b. `b=0, a<0` c. `b >0, a<0` d. `b<<0, a>>0`

If the equation sin^2 x-a sin x + b = 0 has only one solution in (0, pi) then which of the following statements are correct?

If the equation x^4- λx^2+9=0 has four real and distinct roots, then lamda lies in the interval

If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then b//a has the value equal to _____.

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .

If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

If equation 2x^(3)-6x+2sina+3=0,a in (0,pi) has only one real root, then the largest interval in which a lies is

A function f(x) is such that f(x)=0 has 8 distinct real roots and f(4+x)=f(4-x) for x in R . Sum of real roots of the equation f(x)=0 is

If a x^2+b x+6=0 does not have distinct real roots, then find the least value of 3a+bdot

Find the real roots of the equation . x^2+5|x|+6=0

Let a in R and f : R rarr R be given by f(x)=x^(5)-5x+a , then (a) f(x)=0 has three real roots if a gt 4 (b) f(x)=0 has only one real root if a gt 4 (c) f(x)=0 has three real roots if a lt -4 (d) f(x)=0 has three real roots if -4 lt a lt 4