Quadratic Equation
- The expression x2 − x + 1 has :
-
View Hint View Answer Discuss in Forum
According to question , we have
Comparing x2 - x + 1 with ax2 + bx + c , we get
a = 1, b = −1, c = 1
Here D = b2 - 4ac = ( - 1 )2 - 4 (1)(1)
= 1 - 4 = - 3Correct Option: C
According to question , we have
Comparing x2 - x + 1 with ax2 + bx + c , we get
a = 1, b = −1, c = 1
Here D = b2 - 4ac = ( - 1 )2 - 4 (1)(1)
= 1 - 4 = - 3
Since D < 0, so the given expression has no proper linear factor.
- The length of a rectangular plot is 8 m greater than its breadth. If the area of the plot is 308 m2, find the length of the plot.
-
View Hint View Answer Discuss in Forum
Let, the breadth of the rectangular plot be x m. Then the length of rectangular plot = (x + 8) m
∴ Area = Length × Breadth = x(x + 8)m2 But the area of the plot is given to be 308 m2
∴ x( x + 8 ) = 308 ⇒ x2 + 8x - 308 = 0Correct Option: C
Let, the breadth of the rectangular plot be x m. Then the length of rectangular plot = (x + 8) m
∴ Area = Length × Breadth = x(x + 8)m2 But the area of the plot is given to be 308 m2
∴ x( x + 8 ) = 308 ⇒ x2 + 8x - 308 = 0
⇒ x2 + 22x - 14x - 308 = 0
⇒ x( x + 22 ) - 14 ( x - 22 ) = 0
⇒ ( x + 22 ) ( x - 14 ) = 0
⇒ x = 14, -22
But, x = −22 is not possible, since breath cannot be negative
∴ x = 14
Hence the breadth of the rectangular plot = 14 m Length of the rectangular plot = (14 + 8) m = 22 m.
- The value of x in the equation
x + 1 2 - 3 x - 1 = 4 is : x 2 x
-
View Hint View Answer Discuss in Forum
We can say that ,
Putting in above equation , x - 1 = y x ∴ x + 1 2 = x2 + 1 + 2 = x + 1 2 + 4 = y2 + 4 x x2 x Correct Option: C
We can say that ,
Putting in above equation , x - 1 = y x
So, given equation becomes∴ x + 1 2 = x2 + 1 + 2 = x + 1 2 + 4 = y2 + 4 x x2 x ⇒ y y - 3 = 0 ⇒ y = 0 or y = 3 2 2 ∴ x - 1 = 0 ⇒ x - 1 = 3 x x 2
⇒ x2 - 1 = 0 or 2x2 - 3x - 2 = 0
⇒ x = ± 1 or ( 2x + 1 ) ( x - 2 ) = 0
⇒ x = ± 1 or - 1/2 or x = 2.
Thus , option C is correct answer .