Question

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

Answer 1

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.

Answer 2

one root of x²+7x+k = 0 is -2
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