Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2019MathematicsQuadratic Equation

If the equation x^2+p x+q=0 and x^2+q x+p=0 have a common root then p+q+1 is equal to

Options

  1. A0
  2. B1
  3. C2
  4. D-1

Correct answer

A. 0

Step-by-step solution

Given equations are x^2+p x+q=0 ...(i) x^2+q x+p=0 ...(ii) Let be the common root, then aligned & ^2+p +q=0 and ^2+q +p=0 & ^2 p^2-q^2 = q-p = 1 q-p aligned ^2= (p-q)(p+q) -(p-q) =-(p+q) ...(iii) and = q-p q-p =1 ...(iv) From Eq. (iii) aligned & & ^2 & =-p+q & & (1)^2 & =-(p+q) [ from Eq. (iv) ] & & p+q & =-1 p+q+1=0 aligned

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