Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEST2012MathematicsQuadratic Equation

For any real number t belonging to the open interval (0, 1 2 ) consider the quadratic equation p_t(x)= (t-t^2 ) x^2-(1-t) x+t^2=0 in x . Let _t, _t denote the roots of p_t ., Then

Options

  1. A_t and _t are always imaginary.
  2. BFor infinitely many values of t , the corresponding root _t is rational and for infinitely many values of t, _
  3. C_t and _t are real and positive; one of _t and _t is greater than 1 and other is less than 1.
  4. DIf t ( 1 2 )- , then | _t- _t | 0 .

Correct answer

D. If t ( 1 2 )- , then | _t- _t | 0 .

Step-by-step solution

No solution available.

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 NEST PYQs