Question

find the zero of the polynomial 2x² - 3 + 5x​

Answer 1

Answer:

$( 2x + 1)(x + 3)$

Step-by-step explanation:

$2 {x}^{2} + 5x - 3 \\ \\ = 2 {x}^{2} + 6x - x - 3 \\ \\ 2x(x + 3) - 1(x + 3) \\ \\ =( 2x + 1)(x + 3)$

Answer 2

Method:-1

Factorisation

2x² + 5x - 3 = 0

2x² + 6x - x - 3 = 0

2x(x + 3) - 1(x + 3 ) = 0

(2x - 1)(x + 3) = 0

2x - 1 = 0 and x + 3 =0

2x = 1 and x = -3

x = 1/2 and x = -3

Method ;-2

Quadratic Formula

$\sf x = \dfrac{-b\pm\sqrt{b^2-4ac} }{2a}$

Now take Equation

2x² + 5x - 3 = 0

Compare with

ax²+bx+c=0

we get

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

Put the value on formula

$\sf x=\dfrac{-5\pm\sqrt{(5)^{2}-4\times2\times-3 } }{2\times2}$

$\sf x = \dfrac{-5\pm\sqrt{25+24} }{4}$

$\sf x = \dfrac{-5\pm\sqrt{49} }{4}$

$\sf x=\dfrac{-5-7}{4} \:and \:x=\dfrac{-5+7}{4}$

$\sf x = -3 \: and\: x = \dfrac{1}{2}$