Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Determine the range of for which the quadratic equation has no real roots.
MATHEMATICS · Single correct · CBSE · Mathematics · Quadratic Equations · Quadratic Equations
Problem Determine the range of p p p 3 x 2 + ( 2 p − 1 ) x + ( p + 4 ) = 0 3x^{2} + (2p - 1)x + (p + 4) = 0 3 x 2 + ( 2 p − 1 ) x + ( p + 4 ) = 0 p < 4 − 63 2 or p > 4 + 63 2 p < \dfrac{4 - \sqrt{63}}{2}\;\text{or}\;p > \dfrac{4 + \sqrt{63}}{2} p < 2 4 − 63 or p > 2 4 + 63 4 − 63 2 ≤ p ≤ 4 + 63 2 \dfrac{4 - \sqrt{63}}{2} \le p \le \dfrac{4 + \sqrt{63}}{2} 2 4 − 63 ≤ p ≤ 2 4 + 63 4 − 63 2 < p < 4 + 63 2 \dfrac{4 - \sqrt{63}}{2} < p < \dfrac{4 + \sqrt{63}}{2} 2 4 − 63 < p < 2 4 + 63 5 − 69 4 < p < 5 + 69 4 \dfrac{5 - \sqrt{69}}{4} < p < \dfrac{5 + \sqrt{69}}{4} 4 5 − 69 < p < 4 5 + 69 Browse the problem library