Quadratic Equations
Exercise 4.1
Q1. Check whether the following are quadratic equations:
i. (x+1)² =2x-3
Sol: (x+1)² =2x-3
=> x²+2x+1=2x-3. [(a+b)² = a² +b² +2ab)]
=> X²+ 2x+1-2x +3 =0
=> X² + 4 =0
Since, it is in the form of ax² +bx+c=0.
Therefore, the given equation is a quadratic equation.
ii. x²- 2x= (-2) (3-x)
=> X² - 2x = -6 + 2x
=> X² -2x + 6 -2x= 0
=> X² + 6 = 0
Since, it is in the form of ax² +bx+c=0.
Therefore, the given equation is a quadratic equation.
iii. (X-2) (X+1) = (X-1) (X+3)
=> X² +X -2X -2 = X² + 3X -X + 3
=> X² -X -2 -X² -2X + 3 = 0
=> -3x + 1 = 0
Since, it is not in the form of ax² +bx+c=0.
Therefore, the given equation is not a quadratic equation.
iv. (x-3) (2x+1) = x (x+5)
=> 2x² +1x - 6x -3 = X² + 5x
=> 2x² - 5x - 3 -X² - 5x
=> x² - 10x -3 = 0
Since, it is in the form of ax² +bx+c=0.
Therefore, the given equation is a quadratic equation
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