Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201921 Apr 2019Evening ShiftMathematicsQuadratic EquationActual

x ∈ ℝ : 6 + x - x 2 2 x + 5 ≥ 6 + x - x 2 x + 4 =

Options

  1. A[ - 2 , 3 ]
  2. B( - ∞ , - 4 ] ∪ - 5 2 , - 1
  3. C[ - 2 , - 1 ] ∪ 3
  4. D( - ∞ , - 4 ] ∪ [ - 2 , - 1 ]

Correct answer

C. [ - 2 , - 1 ] ∪ 3

Step-by-step solution

It is given that, 6 + x - x 2 2 x + 5 ≥ 6 + x - x 2 x + 4 Rewrite the above equation. ⇒ 6 + x - x 2 1 2 x + 5 - 1 x + 4 ≥ 0 ⇒ 6 + x - x 2 x + 4 - 2 x - 5 ( 2 x + 5 ) ( x + 4 ) ≥ 0 ⇒ 6 + x - x 2 - ( x + 1 ) ( 2 x + 5 ) ( x + 4 ) ≥ 0 ⇒ ( x + 1 ) ( 2 x + 5 ) ( x + 4 ) ≤ 0 Now, x ∈ ( - ∞ , - 4 ) ∪ ( - 5 2 , - 1 ]     . . . i For the expression to exist 6 + x - x 2 ≥ 0 ⇒ x 2 - x - 6 ≤ 0 ⇒ ( x - 3 ) ( x + 2 ) ≤

Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

If is the common root of the quadratic equations x^2-5 x+4 a=0 , x^2-2 a x-8=0 , where a R , then the value of ^4- ^3+68 is 2025If , are the roots of x^2-5 x-6 =0 and , are the roots of x^2-5 x-6 =0 , then + + + = 2025If , , are the roots of the equation x ^3+ px ^2+ qx + r =0 , then ( + )( + )( + )= 2025Let f(x)=x^2+2 b x+2 c^2 and g(x)=-x^2-2 c x+b^2, x R . If b and c are nonzero real numbers such that f(x)> g(x) , then | c b | lies in the interval 2025If x ^2-4 ax +5+ a >0 for all x R whenever a ( , ) , then 4 + = 2025If , , are the roots of the equation x^3-12 x^2+k x-18=0 and one of them is thrice the sum of the other two roots, then ^2+ ^2+ ^2-k= 2025The polynomial equation of degree 5 whose roots are the roots of the equation x^5-3 x^4-x^3+11 x^2-12 x+4=0 each increased by 2, is 2025If the difference of the roots of the equation x^2-7 x+10=0 is same as the difference of the roots of the equation x ^2-17 x + k =0 , then a divisor of k is 2025 Full Quadratic Equation list All AP EAMCET PYQs