Mathematics
Which of the following is a quadratic equation? 1. x^2 - 2√x + 7 = 0 2. 2x^2 - 5x = (x - 1)^2 3. x - (1/x) = 2x^2 4. x^2 + (1x^2) = 2
Answer
Solving,
⇒ 2x2 - 5x = (x - 1)2
⇒ 2x2 - 5x = [(x)2 + (1)2 - 2 × x × 1]
⇒ 2x2 - 5x = x2 + 1 - 2x
⇒ 2x2 - 5x - x2 - 1 + 2x = 0
⇒ 2x2 - x2 - 5x + 2x - 1 = 0
⇒ x2 - 3x - 1 = 0
The highest power of equation is 2 and it's equivalent to ax2 + bx + c = 0 . Hence the equation is a quadratic equation.
Hence, option 2 is the correct option.
Related Questions
If the discriminant of the quadratic equation, ax2 + bx + c = 0, a ≠ 0 is greater than zero and a perfect square and a, b, c are rational, then the roots are:
rational and equal
irrational and unequal
irrational and equal
rational and unequal
If the discriminant of a quadratic equation, ax2 + bx + c = 0, is greater than zero and a perfect square and b is irrational, then the roots are:
irrational and unequal
irrational and equal
rational and unequal
rational and equal
Which of the following is a quadratic equation?
x2 + 1 = (2 - x)2 + 3
2x2 + 3 = (5 + x)(2x - 3)
x3 - x2 = (x - 1)3
none of these