Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KVPY2015MathematicsQuadratic Equation

Two distinct polynomial f ( x ) and g ( x ) are defined as follows: f(x)=x²+a x+2 ; g(x)=x²+2 x+a If the equation f(x)=0 and g(x)=0 have a common root then the sum of the roots of the equation f(x)+g(x)=0 is

Options

  1. A- 1 2
  2. B0
  3. C1 2
  4. D1

Correct answer

C. 1 2

Step-by-step solution

array l f(x)=x²+a x+2 g(x)=x²+2 x+a array Here a common Roat then | array ll 1 & a 1 & 2 array | | array ll a & 2 2 & a array |= | array cc 2 & 1 a & 1 array |² array l = a=2,-3 f(x)+g(x)=2 x²+(a+2) x+a+2 array Sum of roots = -( a +2) 2 if a =-3 then sum = 1 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 KVPY PYQs