Question

Find the roots of the following Quadratic Equations using method of factorization and formula method both.
$(ii) {2x}^{2} - 5x + 3 = 0$

$(i) 2x^{2} - x - 91 = 0$
​

Answer 1

Answer:

x=3/2 and x=1

Step-by-step explanation:

"Roots" means solutions

ii) 2x^2-5x+3

find two numbers that multiply to 6 and add to -5

those 2 numbers are: -3 and -2

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

Factorize out the the common factor

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

Combine the brackets and the numbers outside of brackets  

2x-3=0         x-1=0

x=3/2            x=1

Answer 2

$\sf{\bold{\purple{\star{\underline{\underline{Solution\: 1}}}}}}$

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ 2x^2 - 5x + 3 = 0 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ 2x^2 - 2x - 3x + 3 = 0 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ 2x ( x + 1 ) - 3 ( x + 1 )= 0 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ (2x - 3 ) ( x + 1 ) = 0 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ 2x - 3= 0 | x + 1 = 0 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ 2x = 3 | x = - 1 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ x =\dfrac{3}{2} | x = - 1 }}$

⠀⠀⠀⠀

$\sf{\star{\boxed{\orange{\frak{ x = \dfrac{3}{2} or - 1}}}}}$

⠀⠀⠀⠀

$\sf{\bold{\purple{\star{\underline{\underline{Solution\: 2}}}}}}$

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ 2x^2 - x - 91 = 0 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ 2x^2 - 14x + 13x - 91 = 0 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ 2x ( x - 7 ) + 13 ( x - 7)= 0 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ (2x + 13 ) ( x - 7 ) = 0 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ 2x + 13 = 0 | x - 7 = 0 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ 2x = - 13 | x = 7 }}$

⠀⠀⠀⠀

⠀⠀⠀⠀

$\sf : \implies\:{\bold{ x =\dfrac{-13}{2} | x = 7 }}$

⠀⠀⠀⠀

$\sf{\star{\boxed{\orange{\frak{ x = \dfrac{-13}{2} or 7}}}}}$

⠀⠀⠀⠀