Choose the quadratic equation among these A) x ( x + 1) = 0 B) 2x + 7 = y C) x 2 − x(x + 4) = 0 D) 2(x − 3) = 0
Answers
i)
(x+1)
2
=2(x−3)
x
2
+2x+1=2x−6
x
2
+7=0 → Quadratic
ii)
x
2
−2x=−2(3−x)
x
2
−2x=−6+2x
x
2
+4x+6=0 → Quadratic
iii)
(x−2)(x+1)=(x−1)(x+3)
x
2
−x−2=x
2
+2x−3
3x=1 → Non Quadratic
iv)
(x−3)(2x+1)=(x)(x+5)
2x
2
−5x−3=x
2
+5x
x
2
+10x−3=0 → Quadratic
v)
(x−3)(2x−1)=(x−1)(x+5)
2x
2
−7x+3=x
2
+4x−5
x
2
−11x+8=0 → Quadratic
vi)
x
2
+3x+1=(x−2)
2
x
2
+3x+1=x
2
−4x+4
7x=3 → Non Quadratic
vii)
(x+2)
3
=2x(x
2
−1)
x
3
+8+6x(x+2)=2x
3
−2x
x
3
+8+6x
2
+12x=2x
3
−2x
−x
3
+6x
2
+14x+8=0 → Non Quadratic
viii)
x
3
−4x
2
−x+1
=x
3
+3x
2
(−2)+3x(−2)
2
+(−2)
3
x
3
−4x
2
−x+1=x
3
−6x
2
+12x−8
x
3
−4x
2
−x+1−x
3
+6x
2
−12x+8=0
2x
2
−13x+9=0 → Non Quadratic
SOLUTION
TO CHOOSE THE CORRECT OPTION
Choose the quadratic equation among these
A) x ( x + 1) = 0
B) 2x + 7 = y
C) x² − x(x + 4) = 0
D) 2(x − 3) = 0
CONCEPT TO BE IMPLEMENTED
Quadratic equation :
A quadratic equation is an algebraic expression of the second degree of the variable involved
More precisely Quadratic equations are the polynomial equations of degree 2 in one variable
EVALUATION
CHECKING FOR OPTION : 1
x ( x + 1) = 0
⇒ x² + x = 0
Since the polynomial equations of degree 2 in one variable
This is a quadratic equation
CHECKING FOR OPTION : 2
2x + 7 = y
Since there are two variables
So This is not a quadratic equation
CHECKING FOR OPTION : 3
x² − x(x + 4) = 0
⇒ x² - x² - 4x = 0
⇒- 4x = 0
Since the polynomial equations of degree 1 in one variable
This is not a quadratic equation
CHECKING FOR OPTION : 3
2(x-3) = 0
Since the polynomial equations of degree 1 in one variable
This is not a quadratic equation
FINAL ANSWER
Hence the correct option is A) x( x + 1) = 0
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