Advertisements
Advertisements
Question
Find the roots of the following quadratic equation by the factorisation method:
`3x^2 + 5sqrt(5)x - 10 = 0`
Advertisements
Solution
Given equation is `3x^2 + 5sqrt(5)x - 10` = 0
⇒ `3x^2 + 6sqrt(5)x - sqrt(5)x - 2sqrt(5) * sqrt(5)` = 0 ....[By splitting the middle term]
⇒ `3x^2 + 6sqrt(5)x - sqrt(5)x - 10` = 0
⇒ `3x^2 + 6sqrt(5)x - sqrt(5)x - 2sqrt(5) * sqrt(5)` = 0
⇒ `3x(x + 2sqrt(5)) - sqrt(5) (x + 2sqrt(5))` = 0
⇒ `(x + 2sqrt(5))(3x - sqrt(5))` = 0
Now, `x + 2sqrt(5)` = 0
⇒ x = `- 2sqrt(5)` and `3x - sqrt(5)` = 0
⇒ x = `sqrt(5)/3`
Hence, the roots of the equation `3x^2 + 5sqrt(5)x - 10` = 0 are `-2sqrt(5)` and `sqrt(5)/3`.
APPEARS IN
RELATED QUESTIONS
Solve for x :
`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`
Find the roots of the following quadratic equation by factorisation:
100x2 – 20x + 1 = 0
Solve for x :
`1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x != -1, -1/5, -4`
Find the consecutive numbers whose squares have the sum 85.
A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?
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.
The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m2, what are the length and breadth of the hall?
If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.
Solve : x2 – 11x – 12 =0; when x ∈ N
`3x^2-x-2=0`
The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers.
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Solve the following quadratic equations by factorization: \[\sqrt{3} x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]
In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]
If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =
The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.
Solve the following quadratic equation using factorization method:
`"x"^2-11"x"+24=0`
In each of the following determine whether the given values are solutions of the equation or not
2x2 - 6x + 3 = 0; x = `(1)/(2)`
The length (in cm) of the hypotenuse of a right-angled triangle exceeds the length of one side by 2 cm and exceeds twice the length of another side by 1 cm. Find the length of each side. Also, find the perimeter and the area of the triangle.
Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.
