Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation
Let ( ₂ x )^2-4 ₂ x-m^2-2 m-13=0 be an equation in x and m R , then which of the following must be correct?
Options
- AFor any m R , the equation has two distinct solutions
- BThe product of the solutions of the equation does not depend on m
- COne of the solutions of the equation is less than 1 while the other is greater than 1 for m R
- DThe minimum value of the larger solution is 2^6 and maximum value of the smaller solution is 2⁻²
Correct answer
D. The minimum value of the larger solution is 2^6 and maximum value of the smaller solution is 2⁻²
Step-by-step solution
aligned & ( ₂ x )^2-4 ₂ x-12=(m+1)^2 & t^2-4 t- 12+(m+1)^2 =0 & t= 4 16+4 (12+(m+1)^2 ) 2 aligned D 0 (A) is correct now D_ min when m=-1 gathered ₂ x= 4 8 2 =6 or -2 x=2^6 or 2⁻² gathered (C) and (D) are correct aligned & Also ₂ x₁+ ₂ x₂=4 & ₂ x₁ x₂=4 & x₁ x₂=2^4 aligned