Quadratic Equations Class 11

Quadratic Equations Class 11 – Consider the quadratic equation: \(px^{2}+qx+r=0\) with real coefficients p, q, r and \(p\neq 0\). Now, let us assume that the discriminant d < 0 i.e. \(b^{2}-4ac< 0\). The solution of above quadratic equation will be in the form of complex numbers given by, \(x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}=\frac{-b\pm i\sqrt{4ac-b^{2}}}{2a}\)

  1. Find the roots of equation \(x^{2}+2=0\)

Solution: Give, \(x^{2}+2=0\)

i.e. \(x^{2} = -2\) or x = \(\pm \sqrt{2}i\)

  1. Solve \(\sqrt{5}x^{2}+x+\sqrt{5}=0\)

Solution: Given \(\sqrt{5}x^{2}+x+\sqrt{5}=0\)

Therefore, discriminant D = \(b^{2}-4ac=1-4(\sqrt{5}\times \sqrt{5})=-19\)

Therefore, the solution of given quadratic equation = \(\frac{-1\pm \sqrt{-19}}{2\sqrt{5}}=\frac{-1\pm 19i}{2\sqrt{5}}\)

  1. Solve \(x^{2}+x+1=0\)

Solution: Given \(x^{2}+x+1=0\)

Therefore, discriminant D = \(b^{2}-4ac=1-4=-3\)

Therefore, the solution of given quadratic equation = \(\frac{-1\pm \sqrt{-3}}{2}=\frac{-1\pm 3i}{2}\)

Quadratic Equations Class 11 Examples

Quadratic Equations Class 11
Quadratic Equations Class 11
Quadratic Equations Class 11
Quadratic Equations Class 11
Quadratic Equations Class 11
Quadratic Equations Class 11
Quadratic Equations Class 11


Practise This Question

In a marathon of 5 km, Manish could run for 2 km.If  Kushagra ran for 12 of the total length of the marathon, who covered more distance?