Multiple choice

Find the values of 'p' for which the quadratic equation $\displaystyle { px }^{ 2 }+4x+1=0$ has real roots.

  1. $\displaystyle p\le 4$
  2. $\displaystyle p\ge 6$
  3. $\displaystyle p\ge 4$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
AI explanation

For the quadratic equation px^2 + 4x + 1 = 0 to have real roots, the discriminant must be greater than or equal to zero, meaning b^2 - 4ac >= 0. Substituting the coefficients gives 4^2 - 4(p)(1) >= 0, which simplifies to 16 - 4p >= 0. Solving for p gives 4p <= 16, meaning p <= 4.

Keep practicing — related questions