Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202125 Aug 2021Morning ShiftMathematicsQuadratic EquationActual

Let m and n be two integers such that 0 m 10 and 0 n 10 . Then, the number of ordered pairs (m, n) such that x^2+m x+n=0 has real roots is

Options

  1. A71
  2. B73
  3. C75
  4. D72

Correct answer

B. 73

Step-by-step solution

Given, x^2+m x+n=0 has real roots. array ll m^2-4 n 0 0 m, n 10, m^2 4 n m=10, & n= 0,1,2, , 10 =11 m=9, & n= 0,1,2, , 10 =11 m=8, & n= 0,1,2, , 10 =11 m=7, & n= 0,1,2, , 10 =11 m=6, & n= 0,1,2, , 9 =10 m=5, & n= 0,1,2, , 6 =7 m=4, & n= 0,1,2,3,4 =5 m=3, & n= 0,1,2 =3 m=2, & n= 0,1 =2 m=1, & n= 0 =1 m=0, & n= 0 =1 array Number of order pair of (m, n) is 11+11+11+11+10+7+5+3+2+1+1=73

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