Question

Quadratic Equations:
1. Find the roots of the following:
(i) 2x2-3x+1​

Answer 1

Answer :

As, we have to find the roots of tge polynomial 2x² - 3x + 1.

We know that,

$\Large \star{\boxed{\rm{D = b^2 - 4ac}}}$

Where,

• a = 2
• b = -3
• c = 1

______________[Put Values]

$\implies{\tt{D = (-3)^2 - 4(2)(1)}} \\ \\ \tt{\implies D = 9 - 8} \\ \\ \tt{\implies D = 1} \\ \\ \Large{\star{\boxed{\rm{D = 1}}}}$

$\rule{200}{2}$

Now,

$\Large \star{\boxed{\rm{x = \frac{-b \pm \sqrt{D}}{2a}}}}$

____________[Put Values]

$\tt{\implies x = \frac{-(-3) \pm \sqrt{1}}{2(2)}} \\ \\ \tt{\implies x = \frac{3 \pm 1}{4}} \\ \\ \bf{\dag \: \: \: \:Taking \: positive.} \\ \\ \tt{\implies x = \frac{3 + 1}{4}} \\ \\ \tt{\implies x = 1} \\ \\ \bf{\dag \: \: \: \:Taking \: negative.} \\ \\ \tt{\implies x = \frac{3 - 1}{4}} \\ \\ \tt{\implies x = \frac{1}{2}}$