Question

Find the roots of the polynomials
2x ² - 5x+3​

Answer 1

$\Huge{\underline{\underline{\blue{\mathfrak{Answer :}}}}}$

$\Large{\sf{Given :}}$

2x² - 5x + 3 is a polynomial.

$\rule{200}{2}$

$\LARGE{\sf{To \: Find :}}$

Roots of the equation

$\rule{200}{2}$

$\LARGE{\sf{Solution :}}$

Quadratic formula is given below.

$\LARGE{\boxed{\boxed{\green{\tt{x = \frac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a}}}}}}$

Where,

a = 2, b = -5 and c = 3

(Putting Values)

$\sf{⇒x = \frac{ - ( - 5 )\pm \sqrt{( - {5) }^{2} - 4(2)(3)} }{2(2)} } \\ \\ \sf{⇒x = \frac{5 \pm \sqrt{25 - 24} }{4} } \\ \\ \sf{⇒x = \frac{5 \pm1}{4} } \\ \\ \bf{Now \: \:x \: \: can \: be,} \\ \\ \sf{⇒x = \frac{5 - 1}{4} } \\ \\ \sf{⇒x = \frac{ \cancel4}{ \cancel4} } \\ \\ \sf{⇒x = 1} \\ \\ \bf{Or} \\ \\ \sf{⇒x = \frac{5 + 1}{4} } \\ \\ \sf{⇒x = \frac{6}{4} } \\ \\ \sf{⇒x = \frac{2}{3} }$

$\Large{\boxed{\red{\sf{x \: = \: 1,\frac{2}{3}}}}}$