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Help me please with this equation

Help me please with this equation-example-1

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Answer: The function has two roots in common.

Explanation:

To determine how many roots the function
\( f(x) = x^2 - 4x - 5 \) has, we can find its discriminant. The discriminant will tell us the nature of the roots:

1. If
\( \Delta > 0 \), the quadratic has two distinct real roots.

2. If
\( \Delta = 0 \), the quadratic has one real root (a repeated root).

3. If
\( \Delta < 0 \), the quadratic has no real roots (two complex conjugate roots).

The discriminant
\( \Delta \) for a quadratic equation of the form
\( ax^2 + bx + c \)is given by:


\[ \Delta = b^2 - 4ac \]

For the function
\( f(x) = x^2 - 4x - 5 \):

a = 1

b = -4

c = -5

Plugging in these values:


\[ \Delta = (-4)^2 - 4(1)(-5) \]

Let's calculate the value of
\( \Delta \) to determine the number of roots.

The discriminant
\( \Delta \) for the function
\( f(x) = x^2 - 4x - 5 \) is:


\[ \Delta = 36 \]

Since
\( \Delta > 0 \), the quadratic function
\( f(x) = x^2 - 4x - 5 \) has two distinct real roots.

Thus, the function has two roots in common.

User Harikrishna
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