Advertisements
Advertisements
प्रश्न
Find the roots of the following quadratic equation by the factorisation method:
`3x^2 + 5sqrt(5)x - 10 = 0`
Advertisements
उत्तर
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
संबंधित प्रश्न
Solve the following quadratic equation for x: x2 – 2ax – (4b2 – a2) = 0
Solve for x :
`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
Solve each of the following equations by factorization:
`2x^2-1/2x=0`
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
Solve the following quadratic equations by factorization:
\[9 x^2 - 6 b^2 x - \left( a^4 - b^4 \right) = 0\]
Find the value of k for which the following equations have real and equal roots:
\[x^2 + k\left( 2x + k - 1 \right) + 2 = 0\]
Show that x = −2 is a solution of 3x2 + 13x + 14 = 0.
Find the discriminant of the quadratic equation \[3\sqrt{3} x^2 + 10x + \sqrt{3} = 0\].
If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =
Solve the following equation : `"ax"^2 + (4"a"^2 - 3"b")"x" - 12"ab" = 0`
Solve the following equation: `"a"("x"^2 + 1) - x("a"^2 + 1) = 0`
An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
the return Journey. If the return journey took 30 minutes less than the onward journey write down an equation in x and find its value.
In each of the following determine whether the given values are solutions of the equation or not.
3x2 - 2x - 1 = 0; x = 1
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
Find two consecutive integers such that the sum of their squares is 61
If the product of two positive consecutive even integers is 288, find the integers.
If the sum of two smaller sides of a right – angled triangle is 17cm and the perimeter is 30cm, then find the area of the triangle.
A person was given Rs. 3000 for a tour. If he extends his tour programme by 5 days, he must cut down his daily expenses by Rs. 20. Find the number of days of his tour programme.
