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

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 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 alpha & beta

If the sum of the roots of the quadratic equation a x^2+b x+c=0 is equl to the sum of the squares of their reciprocals, then prove that a/c , b/a a n d c/b are in H.P.

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 _____.

The quadratic equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 has equal roots if

lf the quadratic equations x^2+bx+c=0 and bx^2+cx+1=0 have a common root then prove that either b+c+1=0 or b^2+c^2+1=bc+b+c .

The real roots of the quadratic equation x^(2)-x-1=0 are ___.

If a x^2+(b-c)x+a-b-c=0 has unequal real roots for all c in R ,t h e n

If the equation x^2 + bx + ca = 0 and x^2 + cx + ab = 0 have a common root and b ne c , then prove that their roots will satisfy the equation x^2 + ax + bc = 0 .