Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2019MathematicsQuadratic Equation

Let S = 1 , 2 , 3 , … , 100 . Suppose b and c are chosen at random from the set S . The probability that 4 x 2 + b x + c has equal roots is

Options

  1. A0.001
  2. B0.004
  3. C0.007
  4. D0.01

Correct answer

A. 0.001

Step-by-step solution

The quadratic equation 4 x 2 + b x + c = 0 has equal roots if b 2 - 16 c = 0 ⇒ b 2 = 2 4 c Now, C should be chosen from the set S = 1 , 2 , 3 , … , 100 , such that it is a perfect square number, c = 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 ,49,64,81,100 ∴ number of ordered pair ( b ,   c ) will be 10 . So, required probability = 10 100 × 100 = 1 1000 = 0 . 001

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 KVPY PYQs