find the zeros of the following polynomials and verify the relationship between the zeros and the coefficient 1. x sq. -5, 2. 3x sq. -x -4, 3. 5y sq. +10y, 4. 2x sq. -11x + 15
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1. p(x) = x^2-5
0 = x^2-5
x^2 = 5
x = + root 5 or x = - root 5
therefore, alpha = + root 5
beta = - root 5
converting it to the standard form,
we get,
x^2+0x-5 = 0
by comparing it to standard form,
i.e. ax^2+bx+c = 0
we get, a=1 b=0 c=(-5)
now,
alpha+beta
= +root 5-root 5 = 0 = -0/1 = -b/a
alpha x beta
= root 5 x - root 5 = -5 = -5/1 = c/a
you can do rest of them by this method.GL.
0 = x^2-5
x^2 = 5
x = + root 5 or x = - root 5
therefore, alpha = + root 5
beta = - root 5
converting it to the standard form,
we get,
x^2+0x-5 = 0
by comparing it to standard form,
i.e. ax^2+bx+c = 0
we get, a=1 b=0 c=(-5)
now,
alpha+beta
= +root 5-root 5 = 0 = -0/1 = -b/a
alpha x beta
= root 5 x - root 5 = -5 = -5/1 = c/a
you can do rest of them by this method.GL.
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