The roots of the equation 2x² - 10x + 25 = 0 using quadratic formular method are 5/2 + 5i/2 and 5/2 - 5i/2, the solutions are imaginary.
What are the roots of the equation?
Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;
ax² + bx + c = 0
Where x is the unknown
To solve for x, we use the quadratic formula;
x = (-b±√(b² - 4ac)) / (2a)
Given the data in the question;
2x² - 10x + 25 =0
Compare the equation with the standard form ax² + bx + c = 0
We substitute this values into the quadratic formula above.
x = (-b±√(b² - 4ac)) / (2a)
x = ( -(-10) ± √( (-10)² - [4 × 2 × 25] )) / (2 × 2)
x = ( 10 ± √( 100 - 200 )) / 4
x = ( 10 ± √(-100 )) / 4
Now, we rewrite √(-100) as √-1 × √100
x = ( 10 ± (√-1 × √100) ) / 4
Rewrite √-1 as i
x = ( 10 ± ( i × √100) ) / 4
x = ( 10 ± (i × 10) ) / 4
x = ( 10 ± 10i ) / 4
x = 2( 5 ± 5i ) / 4
x = ( 5 ± 5i ) / 2
Final answer is a combination of both solutions.
x = ( 5 + 5i ) / 2, ( 5 - 5i ) / 2
x = 5/2 + 5i/2, 5/2 - 5i/2
Therefore, the roots of the equation 2x² - 10x + 25 = 0 using quadratic formular method are 5/2 + 5i/2 and 5/2 - 5i/2, the solutions are imaginary.
Learn more about quadratic equations here: brainly.com/question/1863222
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