If α and β are the roots of equation $$ {x^2-2x+4=0}$$, then what is the equation whose roots are ${α^3}\over{β^2}$$ and $${β^3}\over{α^2}$$.

If one root of the equation Ax²+Bx+C = 0 is two and a half times the others, then which of the following is TRUE? 

In solving a problem, one student makes a mistake in the coefficient of the first degree term and obtains – 9 and – 1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was 

If $$ {x^2-12x+33=0}$$, then what is the value of $${(x-4)^2+[{1\over({x-4})^2}}]$$.

What are the roots of the quadratic equations?

  $$(x^2 + 3x - 154 = 0)$$

What are the roots of the equation log₁₀(x²-6x+45) =2?

If the difference between the roots of the equation Ax²+BX+C = 0 is 4, then which of the following is TRUE?

Factor of $$ {12x^{2}+7y^{2}-12}$$ is__