Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
x2 - x - a(a + 1) = 0
Advertisements
उत्तर
We have been given
x2 - x - a(a + 1) = 0
x2 + ax - (a + 1)x - a(a + 1) = 0
x(x + a) - (a + 1)(x + a) = 0
(x - (a + 1))(x + a) = 0
Therefore,
x - (a + 1) = 0
x = (a + 1)
or,
x + a = 0
x = -a
Hence, x = a + 1 or x = -a
APPEARS IN
संबंधित प्रश्न
Solve for x : `(x+1)/(x-1)+(x-1)/(x+2)=4-(2x+3)/(x-2);x!=1,-2,2`
Solve the following quadratic equations by factorization:
5x2 - 3x - 2 = 0
Solve the following quadratic equations by factorization:
`2/2^2-5/x+2=0`
Solve the following quadratic equations by factorization:
`x^2-4sqrt2x+6=0`
Solve the following quadratic equations by factorization:
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1
The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction?
Solve for x: `3x^2-2sqrt3x+2=0`
Solve the following quadratic equation by factorisation.
25m2 = 9
Solve the following quadratic equations by factorization:\[\frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x}; x \neq 0, 2, 3\]
Find the values of k for which the roots are real and equal in each of the following equation:\[px(x - 3) + 9 = 0\]
Solve the following equation: 25x (x + 1) = -4
Solve the following equation:
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 5/2 , x ≠-1/2`
Three consecutive natural numbers are such that the square of the first increased by the product of other two gives 154. Find the numbers.
Solve the following quadratic equation by factorisation:
(x - 4) (x + 2) = 0
Solve the equation:
`6(x^2 + (1)/x^2) -25 (x - 1/x) + 12 = 0`.
In each of the following, determine whether the given values are solution of the given equation or not:
x2 + x + 1 = 0; x = 0; x = 1
Use the substitution y = 3x + 1 to solve for x : 5(3x + 1 )2 + 6(3x + 1) – 8 = 0
The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
In the centre of a rectangular lawn of dimensions 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m2 [see figure]. Find the length and breadth of the pond.
