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Thank you We sneak in and here's your smoke toos

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your brought to you by negative roots there Not a

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fan of the latest dye job What's The negative route

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of the quadratic function F of x equals two x

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squared plus nine x minus thirty five And here the

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potential answer All right so this problem wants us to

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find a negative route of a given function All right

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well we should start by factoring the suckers Get it

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its roots All right Well the first thing that shouldn't

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jump out at us is the two coefficient in front

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of our x squared term there Why Well because instead

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of looking for two numbers that multiply to give us

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negative thirty five like we usually would we instead need

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two numbers that multiply to give us negative seventy court

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two times as much to remember Those two numbers need

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tto add up to nine match our middle term narrowing

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our options here Good thing Well we've got ten and

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negative seven or negative Ten and positive seventh but neither

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of those was a nun Well what about negative fourteen

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Five Who Closer Well there's no combination and negative Fourteen

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and five It gives us nine But if we switch

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the minus sign to the other guy while fourteen plus

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negative five totally adds up to nine Now we can

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factor way Start with f ax equals two x squared

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plus fourteen x minus five x minus thirty five and

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new little grouping to get f of x equals two

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acts times the quantity x plus seven minus five times

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the quantity x plus seven Then we factor we explosive

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from both terms and we get f of x equals

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the quantity to x minus five times the quantity x

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plus seven go now it could solve for both routes

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but we only want the negative one here The first

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set of prints sees is going to lead us to

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a positive number so we just zero in on the

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second one and if x plus seven equals zero and

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Acts would equal negative 7 answer choice eh We're pretty

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proud of ourselves for attacking this problem so ruthlessly No

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