Question

Determine nature of roots of the quadratic equations.
2x² - 5x + 7 = 0 ​

Answer 1

$\huge\underline\frak{\fbox{AnSwEr :-}}$

Compare 2x² - 5x + 7 = 0 with

ax² + bx + c = 0

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies$ a = 2, b = -5 , c = 7 ,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies$ b² - 4 ac = (-5)² - 4 x 2 x 7

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies$ D = 25 - 56

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies$ D = -31

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies$ b² - 4 ac < 0

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\implies$ the roots of the equation are not real

Answer 2

$\Huge{\red{\underline{\textsf{Answer}}}}$

$\rm 2x^2-5x+7=0$

$\rm ax^2+bx+c=0$

a = 2, b = 5, c = 7,

∴ b² - 4ac

$\implies\rm (-5)^2-4(2)(7)$

$\implies\rm 25-56$

$\implies\rm -31$

∴ The Roots do not exist or they are imaginary.