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

If (a^(2)-14a+13)x^(2)+(a+2)x-2=0 does not have two distinct real roots, then the maximum value of a^(2)-15a is _________.

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 equations x^2+a x+12=0. x^2+b x+15=0a n dx^2+(a+b)x+36=0, have a common positive root, then find the values of aa n dbdot

If c is positive and 2a x^2+3b x+5c=0 does not have aby real roots, then prove that 2a-3b+5b>0.

If the quadratic equation a x^2+b x+6=0 does not have real roots and b in R^+ , then prove that a > m a x{(b^2)/(24),b-6}

If x^(4) + 2kx^(3) + x^(2) + 2kx + 1 = 0 has exactly tow distinct positive and two distinct negative roots, then find the possible real values of k.

If the equation 2x^2+k x y+2y^2=0 represents a pair of real and distinct lines, then find the values of kdot

If a and b(!=0) are the roots of the equation x^2+a x+b=0, then find the least value of x^2+a x+b(x in R)dot

If the roots of the equation x^2-8x+a^2-6a=0 are real and distinct, then find all possible value of adot

If x^2+3x+5=0a n da x^2+b x+c=0 have common root/roots and a ,b ,c in N , then find the minimum value of a+b+c