What is the product of the roots of the equation $-2x^2+3x+8=0$ ?

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Answer 1 · 2016-12-17T09:58:31

-4

for any quadratic

$ax^2+bx+c=0" "$ if the roots are $" "alpha" "&" "beta$

the sum of roots $" "alpha+beta=-b/a$

the product of the roots $" "alphabeta=c/a$

these results do need to be memorised.

**see proof below.

for $-2x^2+3x+8=0$

product of roots $" "aplhabeta=8/-2=-4$

*proof of results

$ax^2+bx+c=0" "$ if the roots are $" "alpha" "&" "beta$

$(x-alpha)(x-beta)=0$

expanding

$x^2-betax-alphax+alphabeta=0$

$x^2color(red)(-(alpha+beta))x+color(blue)(alphabeta)=0" "---(1)$

$ax^2+bx+c=0" "$

$-:a$

$=>x^2+color(red)((b/a))x+color(blue)(c/a)=0" "---(2)$

comparing $""--(1)" "&""--(2)" "$ the results follow.