Advertisements
Advertisements
Question
`3x^2-x-2=0`
Advertisements
Solution
`3x^2-x-2=0`
`9x^2-3x-6=0` (Multiplying both sides by 3)
`9x^2-3x=6`
`(3x)^2-2xx3x xx1/2+(1/2)^2=6(1/2)^2` [Adding `(1/2)^2` on both sides]
`(3x-1/2)^2=6+1/4=25/4=(5/2)^2`
`3x-1/2=+-5/2` (Taking square root on both sides)
`3x-1/2=5/2 or 3x-1/2=-5/2`
`3x=5/2+1/2=6/2=3 or =-5/2+1/2=-4/2=-2`
`x=1 or x=-2/3`
Hence, 1 and `-2/3` are the roots of the given equation.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
48x2 − 13x − 1 = 0
Solve the following quadratic equations by factorization:
`x^2-(sqrt3+1)x+sqrt3=0`
Solve the following quadratic equations by factorization:
`m/nx^2+n/m=1-2x`
The sum of two numbers is 48 and their product is 432. Find the numbers?
A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?
An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.
Solve:
`1/p + 1/q + 1/x = 1/(x + p + q)`
Solve the following quadratic equations by factorization:
`2(x^2 – 6) = 3 ( x – 4)`
Solve the following quadratic equation for x:
x2 − 4ax − b2 + 4a2 = 0
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
Solve equation using factorisation method:
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
Solve the following equation by factorization
`sqrt(3x + 4) = x`
Find two consecutive integers such that the sum of their squares is 61
Find two consecutive even natural numbers such that the sum of their squares is 340.
The perimeter of a rectangular plot is 180 m and its area is 1800 m2. Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.
A dealer sells a toy for ₹ 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy.
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
If x = 3 is one root of the quadratic equation 2x2 + px + 30 = 0, find the value of p and the other root of the quadratic equation.
If α and β are roots of the quadratic equation x2 – 7x + 10 = 0, find the quadratic equation whose roots are α2 and β2.
For quadratic equation `2x + 5/x = 5` :
