Pregunta
If 2 is a root of
find we whe of
and hence the otber rovt
Fer what valuzis) of
witl the equation
bave real roors
Fer what valuzis) of
Ask by Stewart Bryant. in South Africa
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
- The other root of the first equation is 150.
- The quadratic equation in
has real roots for all real values of .
Solución
Given that 2 is a root of the equation
we substitute
into the equation:
Step 1. Simplify the equation:
Step 2. Solve for
:
With
, the equation becomes:
We can divide the entire equation by 2:
Since 2 is a known root, let the other root be
. The sum of the roots of a quadratic
is given by:
which leads to:
Now, consider the second part of the problem. We need to find for what values of
the equation
has real roots.
Step 3. Identify the coefficients for the quadratic in
:
Step 4. Compute the discriminant
:
Step 5. Factor out the constant:
Step 6. Analyze the quadratic
. Its discriminant is:
Since
and the coefficient of
is positive, the quadratic
is always positive for all real
.
Thus,
Final Answers:
- The value of
is and the other root of the first quadratic is . - The quadratic equation in
has real roots for all real values of .
Respondido por UpStudy AI y revisado por un tutor profesional
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The Deep Dive
To find
when 2 is a root of
, substitute
. The equation becomes
. Now, simplify it to
. The discriminant (
) must be non-negative for real roots. Here, it’s
, indicating no real values for
.
Next, for the equation
to have real roots, the discriminant must be non-negative:
. This simplifies to
. Factoring out gives us
. Hence,
or
for real roots.

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