Question

verify the relationship between the zeros and coefficients of the following polynomial 1. 2x^2+x-6​

Answer 1

Have a look into attached picture.

Answer 2

$Let \: p(x) = 2x^{2} + x - 6$

We get zeroes of the polynomial p(x) we will take p(x) = 0

$2x^{2} + x - 6 = 0$

/* Splitting the middle term, we get */

$\implies 2x^{2} +4x - 3x - 6 = 0$

$\implies 2x( x + 2) - 3(x + 2 ) = 0$

$\implies (x+2)(2x-3) = 0$

$\implies x+2 = 0 \: Or \: 2x-3 = 0$

$\implies x = -2 \: Or \: 2x = 3$

$\implies x = -2 \: Or \: x = \frac{3}{2}$

$\therefore The \: zeroes \: polynomial \: is \: -2$

$\:and \:\frac{3}{2}$

Verification:

$i) Sum \:of \:the \: zeroes$

$= -2 + \frac{3}{2}$

$= \frac{ -4+3}{2}$

$= \frac{-1}{2}$

$= \frac{- ( Coefficient \:of \:x)}{ ( Coefficient \:of \:x^{2})}$

$ii) Product \:of \:the \: zeroes$

$= -2 \times \frac{3}{2}$

$= -3$

$= \frac{-3}{1}$

$= \frac{Constant \:term}{ ( Coefficient \:of \:x^{2})}$

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