If  $$  \left( x^2+{1\over x^2} \right)- \left( x - {1\over 4} \right)- 7 =0 $$ then two value of x are :

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 

Direction: In the following questions two equations numbered I and II are given. You have to solve both the equations and Give answer

Give answer (A) If x > y
Give answer (B) if x ≥ y
Give answer (C) if x<y
Give answer (D) If x ≤ y
Give answer (E) if x=y or the relationship cannot be established.

 I. x² – 7x+ 12=0
II. y²-12y+32 =0

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

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? 

If α and β are the roots of equation x² - 2x + 4 - 0, then what is the equation whose roots are α³/β² and β³/α²?

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

Direction: In the following questions two equations numbered I and II are given. You have to solve both the equations and Give answer

Give answer (A) If x > y
Give answer (B) if x ≥ y
Give answer (C) if x<y
Give answer (D) If x ≤ y
Give answer (E) if x=y or the relationship cannot be established.

I.  5x+2y=31
II. 3x+7y=36