Answer:
The sum of the roots is 0.5
Step-by-step explanation:
<u><em>The correct question is</em></u>
What is the sum of the roots of 20x^2-10x-30
we know that
In a quadratic equation of the form
The sum of the roots is equal to
in this problem we have
so
substitute
<u><em>Verify</em></u>
Find the roots of the quadratic equation
The formula to solve a quadratic equation is equal to
substitute
The roots are x=-1 and x=1.5
The sum of the roots are
----> is ok
• Angles DXC and AXB form a vertical pair, so they are congruent and have the same measure.
• ∆ABD is isosceles, since it's given that AD and BD are congruent. This means the "base angles" BAD and ABD have the same measure; call this measure <em>x</em>.
• The measure of angle ADB can be computed by using the inscribed angle theorem, which says
m∠ADB = 1/2 (100°) = 50°
(that is, it's half the measure of the subtended arc AB whose measure is 100°)
• The interior angle to any triangle sum to 180° in measure. So we have in ∆ABD,
m∠ADB + 2<em>x</em> = 180°
Solve for <em>x</em> :
50° + 2<em>x</em> = 180°
2<em>x</em> = 130°
<em>x</em> = 65°
• Use the inscribed angle theorem again to find the measure of angle BAC. This will be half the measure of the subtended arc BC, so
m∠BAC = 1/2 (50°) = 25°
• Now in ∆ABX, we have
m∠AXB + 25° + 65° = 180°
m∠AXB = 90°
Hence m∠DXC = 90°.
