Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2013MathematicsQuadratic Equation

If b 0 , then the roots x₁ and x₂ of the equation 2 x^2+6 x+b=0 , satisfy the condition ( x₁ x₂ )+ ( x₂ x₁ ) K , where K is equal to

Options

  1. A2
  2. B-2
  3. C0
  4. D4

Correct answer

B. -2

Step-by-step solution

The discriminant of the quadratic equation 2 x^2+6 x+b=0 is given by D=36-8 b 0 . Therefore, the given equation has real roots. we have, x₁ x₂ + x₂ x₁ = x₁^2+x₂^2 x₁ x₂ = (x₁+x₂ )^2-2 x₁ x₂ x₁ x₂ = (-3)^2-2(b / 2) (b / 2) = 18 b -2 -2 [ b 0]

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 Manipal MET PYQs