Question

if the equation ax²+bx+c=0 and x²+2x+3=0 have a common root then a:b:c =?​

Answer 1

Step-by-step explanation:

$We \: observe \: that \: the \: equation \: {x}^{2} + 2x + 3 = 0 \\ has \: imaginary \: roots \: as \: its \: discriminant \: is \: less \: than \: zero. \: \\ So \:, given \: equation \: have \: all \: common \: roots. \\ \frac{a}{1} = \frac{b}{2} = \frac{c}{3} \\ a \: : \: b \: : \: c = 1 \: : \: 2 \: : \: 3 \: \: \\ Hope \: it \: will \: help \: you.$

Answer 2

$\huge\star{\bold{\underline{\boxed{\tt{\red{Answer}}}}}}\star$

$\large\star\star{\underline{\underline{\boxed{\blue{\mathfrak{Explanation}}}}}}\star\star$

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$\huge\star\star\star\star\star$

$\large{\bold{a{x}^{2}+bx+c=0}}$............$\huge\star$1

$\large{\bold{{x}^{2}+2x+3=0}}$...............$\huge\star$2

$\huge\star\star\star\star\star$

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$\huge\star$1 & $\huge\star$2 have one common roots

Discriminant

=b²-4ac

=2²-4*1*3

=4-12

=-8

here -8<0

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$\huge\star$so roots are imaginary

therefore so both equation have both roots in common

$\bold{\frac{a}{1}=\frac{b}{2}=\frac{c}{3}=k}$

$\huge\arrow$a=k

$\huge\arrow$b=2k

$\huge\arrow$c=3k

$\huge\star\star\star$a:b:c=1:2:3$\huge\star\star\star$