Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2021 · Mathematics · Quadratic Equation

The quadratic equation 3 x^2-(k^2+5 k) x+3 k^2-5 k=0 has real roots...

The quadratic equation 3x2−(k2+5k)x+3k2−5k=03 x^2-\left(k^2+5 k\right) x+3 k^2-5 k=0 has real roots of equal magnitude and opposite sign. Which one of the following is correct?

Options

  1. A0<k<530 < k < \frac{5}{3}
  2. B0<k<350 < k < \frac{3}{5} only
  3. C35<k<53\frac{3}{5} < k < \frac{5}{3}
  4. DNo such value of kk exists

Correct answer

D. No such value of kk exists

Step-by-step solution

If the roots of ax2+bx+c=0a x^2+b x+c=0 are equal in magnitude but opposite in sign then a>0,b=0andc<0a > 0, b=0 and c < 0. ∴k2+5k=0⇒k=0,−5\therefore k^2+5 k=0\Rightarrow k=0,-5 ....(i) 3k2−5k<0⇒k(3k−5)<0\begin{aligned} & 3 k^2-5 k < 0 \\ & \Rightarrow k(3 k-5) < 0\end{aligned}\Rightarrow 0 < k < \frac{5}{3}....(ii)So,noanyvalueof....(ii) So, no any value ofk$ which satisfied (i) and (ii).
Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

For a given k , what is the minimum value of x^2+kx+k^2 ? NDA 2026If the highest degree coefficient is equal to 1 , then what is the total number of… NDA 2026Let α and β be the roots of the quadratic equation x^2-2bx+c^2=0 where b , c are positive… NDA 2026Consider the following statements : I. x + x+1=0 has two irrational roots. II. 5 x -x-4=0… NDA 2026For the following two (02) items: Let f(x) = ax^2 + bx + c be a quadratic polynomial such… NDA 2025For the following two (02) items: Let α and β be the roots of the quadratic equation x^2… NDA 2025For the following two (02) items: Let f(x) = ax^2 + bx + c be a quadratic polynomial such… NDA 2025If one root of the equation x^2 - kx + k = 0 exceeds the other by 2 3 , then which one of… NDA 2025For the following two (02) items: Let α and β be the roots of the quadratic equation x^2… NDA 2025If x = (1111)_2 , y = (1001)_2 and z = (110)_2 , then what is x^3 - y^3 - z^3 - 3xyz… NDA 2025If x^2 - x + 1 = 0 , then what is (x - (1)/(x))^2 + (x - (1)/(x))^4 + (x - (1)/(x))^8… NDA 2025If x + (5)/(y) = 4 and y + (5)/(x) = -4 , then what is (x + y) equal to? NDA 2025For the following two (02) items: Consider the equation abx^2 + bcx + ca = cax^2 + abx +… NDA 2025For the following two (02) items: Consider the equation abx^2 + bcx + ca = cax^2 + abx +… NDA 2025If n is a root of the equation x^2+p x+m=0 and m is a root of the equation x^2+p x+n=0… NDA 2024The roots of the equation 7 x^2-6 x+1=0 are α and β , where 2 α and 2 β are the angles of… NDA 2024 Full Quadratic Equation list Quadratic Equation JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs