which one is the quadratic equations?
Answers
Answer:
A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable. One absolute rule is that the first constant "a" cannot be a zero.
Complete Question :- Which of the following options represents a quadratic equation ?
A) 2(x - 1)² = 4x² -2x + 1
B) 2x - x² = x² + 5
C) 3x² - 3x + 3 = 0
D) All of these
Solution :-
We know that, any equation which can be written in the form of ax² + bx + c = 0 where a ≠ 0 is known as a quadratic equation .
So, checking given options we get,
A) 2(x - 1)² = 4x² -2x + 1
→ 2(x² + 1 - 2x) = 4x² - 2x + 1
→ 2x² - 4x + 2 = 4x² - 2x + 1
→ 4x² - 2x² - 2x + 4x + 1 - 2 = 0
→ 2x² + 2x - 1 = 0
as we can see that, it is in the form of ax² + bx + c = 0 where a ≠ 0 . Therefore, It represents a quadratic equation .
B) 2x - x² = x² + 5
→ x² + x² + 5 - 2x = 0
→ 2x² - 2x + 5 = 0 .
as we can see that, it is in the form of ax² + bx + c = 0 where a ≠ 0 . Therefore, It represents a quadratic equation .
C) 3x² - 3x + 3 = 0
as we can see that, it is in the form of ax² + bx + c = 0 where a ≠ 0 . Therefore, It represents a quadratic equation .
Hence, Option (D) all of the above is correct answer .
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solution of x minus Y is equal to 1 and 2 X + Y is equal to 8 by cross multiplication method
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