If `ax^2 + bx + c` is a perfect square, then prove that b' `b^2=4ac`

If ax^(2)+bx+c is a perfect square,then prove that b backslash b^(2)=4ac

If x is a natural number.If x^2+ax+b is a perfect square prove that a^2=4b .

If the roots of the equation ax^2 + bx + c = 0 are in the ratio 2:3 , then prove that 6b^2 = 25ac

If one root of the equation ax^2+bx+c=0 is the square of the other, prove that , b^3+ac^2+a^2c=3abc .

If one root of the equation ax^2+bx+c=0 is square the other root, then prove that b^3+ac^2+a^2c= 3abc .

If x^(4)+2x^(3)+ax^(2)+bx+9 is a perfect square, where a and b are positive real numbers, then the value of a and b are:

If one root of the equation ax^(2)+bx+c=0 is the square of the other,prove that b^(3)+ac^(2)+a^(2)c=3abc

If the sum of the roots of the quadratic equation ax^(2)+bx+c=0 be equal to the sum of their squares, then prove that 2ac=ab+b^(2) .