Question

The roots of quadratic equation 5x2 – 4x + 5 = 0 are

Real & Equal


Real & Unequal


Not real and equal


Non real and unequal

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{5x^2-4x+5=0}$

$\underline{\textbf{To find:}}$

$\textsf{Nature of roots of the equation}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{5x^2-4x+5=0}$

$\mathsf{Here,\;a=5,\;b=-4,\;c=5}$

$\begin{array}{rl}\mathsf{Discriminant}&\mathsf{=b^2-4ac}\\\\&\mathsf{=(-4)^2-4(5)(5)}\\\\&\mathsf{=16-100}\\\\&\mathsf{=-84\,<\,0}\end{array}$

$\implies\mathsf{Discriminant\,<\,0}$

$\therefore\textbf{Roots are non-real and unequal}$