Question

one of the roots of the equation x^2+px+3=0 is 1. its other root is

Answer 1

$if \: \alpha \: and \: \beta \: are \: roots \: then$
$\alpha \beta = \frac{c}{a} \\ 1 \times \alpha = 3 \\ \alpha = 3$
other root is 3




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Answer 2

According to Remainder & Factor theorm,
$\: \: \: \: \: \: \: p( - 1) = 0 = {( - 1)}^{2} + p \times 1 + 3 \\ = > 1 + p + 3 = 0 \\ = > p = ( - 4).$
Now we have to guess the factor so that p(a) =0.
So,
Try to put values below the constant terms.
So,
Here,
P(1) is coming 0.
$\: \: \: \: \: \: \: p( 1) = {( 1)}^{2} + p \times 1 + 3 \\ = 1 + ( - 4) + 3 = 0 \\ = > 0.$
So,
Other root is (-1).



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