If x = -2 is the root of the equation and is also the zero of the polynomial then find the value of k. - Wired Faculty

Coordinate Geometry

Question

If x = -2 is the root of the equation $square root of 5 space left parenthesis x plus p right parenthesis equals 0$ and is also the zero of the polynomial $px squared plus kx plus 2 square root of 2 comma$ then find the value of k.

Solution

space space space space square root of 2 left parenthesis x plus p right parenthesis equals 0 rightwards double arrow space space x plus p space equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space vertical line space because space square root of 2 not equal to 0 rightwards double arrow space x space equals space minus p

According to the question.
- p = - 2

rightwards double arrow space space space space

p = 2
Let f(x) = px²+ kx +

2 square root of 2

Then, f(x) = 2x²+ kx +

2 square root of 2

If x = -2 is a zero of f(x), then f(-2) = 0

rightwards double arrow space space space space space 2 left parenthesis negative 2 right parenthesis squared space plus space straight k left parenthesis negative 2 right parenthesis space plus space 2 square root of 2 space equals space 0 rightwards double arrow space space space space 2 straight k space equals space 8 space plus space 2 square root of 2 rightwards double arrow space space space space space straight k space equals space 4 plus square root of 2

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