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The error made by zacharias in solving the quadratic equation 0 = -2x² + 5x - 3 using quadratic formula is; the 2 in the numerator should be –2.
<h3>Quadratic equation</h3>There are four methods of solving quadratic equation. Namely;
- Factorization method
- Completing the square method
- Graphical method
- Formula method
0 = -2x² + 5x - 3
- Using quadratic formula
x = -b ± √b² - 4ac / 2a
where,
- a = -2
- b = 5
- c = -3
x = -b ± √b² - 4ac / 2a
x = -5 ± √5² - 4(-2)(-3) / 2(-2)
= -5 ± √25 - (24) / -2
= -5 ± √1 / -2
= -5/2 ± 1/2
= -5/2 - 1/2 or x = -5/2 + 1/2
= -5-1 / 2 or -5+1/ 2
x = -6/2 or -4/2
x = -3 or -2
Therefore, the solution to the quadratic equation is x = -3 or -2
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The time taken by the first and the second train is 1 hour 40 minutes and 1 hour 25 minutes. Then the time when the second train at Niles junction is 5:55 p.m.
<h3>What is speed?</h3>The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
A train leaves Thorn junction at 1:25 p.m. and arrives in Niles at 3:05 p.m. the train makes two stops along the route for a total of 15 minutes.
A second train leaves Thorn junction at 4:30 p.m. and heads to Niles.
This train does not make any stops.
Let the speed of both trains be equal.
Then the time taken by the first train will be
t₁ = 3:05 p.m. - 1:25 p.m.
t₁ = 1 hour 40 minutes
Then the time taken by the second train will be
t₂ = 1:40 - 00:15
t₂ = 1:25 = 1 hour 25 minutes
The time when the second train is at Niles junction will be
→ 4:30 p.m. + 1:25
→ 5:55 p.m.
More about the speed link is given below.
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