find the values of `lambda` such that the equation `tan^2x+lambdatanx+4=0` has atleast one real root

Find the values of k so that the quadratic equation x^(2)+2(k-1)x+k+5=0 has atleast one positive root

Find the values of k so that the quadratic equation x^(2)+2(k-1)x+k+5=0 has atleast one positive root.

Find the set of values of lambda for which the equation |x^(2)-4|x|-12]=lambda has 6 distinct real roots.

The real values of lambda for which the equation,4x^(3)+3x^(2)-6x+lambda=0 has two distinct real roots in [0,1] lie in the interval (A)(0,oo)(B)(3,oo)(C)(-5,(7)/(4))(D)[0,(7)/(4))

The equation 3x^(2)+4ax+b=0 has atleast one root in (0, 1) if :

Find the values of 'm' for which the equation x^4-(m-3)x^2+m =0 has No real roots

Find the integral values of a for which the equation x^4-(a^2-5a+6)x^2-(a^2-3a+2)=0 has only real roots

Find the value of k for which the given equation 9x^(2) + 3kx + 4 = 0 has real and equal roots.

Find the values of p fro which the qadratic equation 2x^(2)+px+8=0 has real roots.

Show that the equation 2x^(2)-6x+3=0 has real roots and find these roots.