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Furkat [3]
3 years ago
5

Write the polynomial as the product of linear factors. h(x) = x^2 ? 2x + 10

Mathematics
1 answer:
miss Akunina [59]3 years ago
4 0

Answer:

If h(x) = x^2 + 2x + 10 then (x+1-3i)*(x+1+3i).

If h(x) = x^2 - 2x + 10 then (x-1-3i)*(x-1+3i).

Step-by-step explanation:

In order to write the polynomial as the product of linear factors, we need to find the roots of the polynomial. A quadratic equation is defined as:

ax^2+bx+c

Because the given polynomial expression is a quadratic equation, we can use the following equations for calculating the roots:

x1=(-b/2a)+\sqrt{b^2-4ac}/2a

x1=(-b/2a)-\sqrt{b^2-4ac}/2a

Since the second term sign is not given, then we can write the expression as:

x^2+s2x+10, in which a=1, b=s2 where 's' represents a sign (- or +), and c=10.

Using the equation for finding the roots we obtain:

x1=(-sb/2a)+\sqrt{b^2-4ac}/2a

x1=(-s2/2*1)+\sqrt{2^2-4*1*10}/(2*1); notice that (sb)^{2} = 2^{2}

x1=(-s1)+\sqrt{-36}/2

x1=-(s1)+6i/2

x1=-(s1)+3i

x2=(-sb/2a)-\sqrt{b^2-4ac}/2a

x2=(-s2/2*1)-\sqrt{2^2-4*1*10}/(2*1); notice that (s2)²=2^2

x2=(-s1)-\sqrt{-36}/2

x2=-(s1)-6i/2

x2=-(s1)-3i

If we consider 's' as possitive (+) the roots are:

x1=-1+3i and x2=-1-3i

Whereas if we consider 's' as negative (-) the roots are:

x1=1+3i and x2=1-3i

The above means that if the equation is h(x) = x^2 + 2x + 10, then we can express the polynomial as: (x+1-3i)*(x+1+3i).

But, if the equation is h(x) = x^2 - 2x + 10, then we can express the polynomial as: (x-1-3i)*(x-1+3i).

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