Question

Factorize the following using splitting the middle term

Whoever does this will receive brainliest​

Answer 1

$\huge\underline\bold{AnswEr:}$

( - x - 1 ) ( 2x - 3 )

$\huge\underline\bold{ExplanaTion:}$

$\large\bold{Given-}$

• -2x² + x + 3

$\large\bold{To\:find-}$

• factors

$\large\bold{Solution-}$

Product = -6

Sum = 1

Factors = 3, -2

: $\implies$ -2x² + 3x - 2x + 3

: $\implies$ -x ( 2x - 3 ) - 1 ( 2x - 3 )

: $\implies$ ( - x - 1 ) ( 2x - 3 )

Hence, our required factors are : ( - x - 1 ) ( 2x - 3 )

$\rule{200}2$

Answer 2

SoLuTiOn :-

$\implies \: - 2 {x}^{2} + x + 3 = 0 \\ \\ \implies \: - 2 {x}^{2} + 3x - 2x + 3 = 0 \: \\ \\ \implies \: - x(2x - 3) - 1(2x - 3) = 0 \\ \\ \implies \: ( - x - 1)(2x - 3) = 0 \\ \\ \implies \: ( - x - 1) = 0 \: or \: (2x - 3) = 0 \\ \\ \implies \: x = - 1 \: or \: x = \frac{3}{2}$

Hence,

Zeroes are -1 or 3/2

Now,

Verification :-

On putting x = -1

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

Now,

On putting x = 3/2

$\implies \: - 2 \times { (\frac{3}{2} )}^{2} + \frac{3}{2} + 3 = 0 \\ \\ \implies \: \frac{ - 18}{4} + \frac{3 \times 2}{2 \times 2} + \frac{3 \times 4}{1 \times 4} = 0 \\ \\ \implies \: \frac{ - 18}{4} + \frac{18}{4} = 0 \\ \\ \implies \: 0 = 0$

Hence Verified.