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Q1.If one root of the equation xsquare+7x+k=0 is -2 ,then find the value of k and the other root.

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by shab

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by shab

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If -2 is the root of the equation x² + 7x + k = 0; then

(-2)² + 7×(-2) + k = 0

⇒ 4 - 14 + k = 0

⇒ -10 + k = 0

⇒**k = 10**

the equation is x² + 7x + 10 = 0.

let the other root is β.

we know that sum of roots is -b/a, that is -7/1 = -7.

⇒ β + (-2) = -7

⇒ β - 2 = -7

⇒ β = -7 + 2

⇒**β = -5**

So other root is -5.

(-2)² + 7×(-2) + k = 0

⇒ 4 - 14 + k = 0

⇒ -10 + k = 0

⇒

the equation is x² + 7x + 10 = 0.

let the other root is β.

we know that sum of roots is -b/a, that is -7/1 = -7.

⇒ β + (-2) = -7

⇒ β - 2 = -7

⇒ β = -7 + 2

⇒

So other root is -5.

therefore, (-2)² + 7(-2)+k = 0

4 - 14 + k = 0

k = 10

The equation is x²+7x+10 = 0

Product of the roots = αβ = 10

(-2) β = 10

β = -5

the other root is -5