Advertisements
Advertisements
Question
Solve the following equation by factorisation :
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Advertisements
Solution
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
⇒ `sqrt(3)x^2 + 3x + 7x + 7sqrt(3)` = 0
⇒ `sqrt(3)x(x + sqrt(3)) + 7(x + sqrt(3))` = 0
⇒ `(x + sqrt(3))(sqrt(3) + 7)` = 0
Either `x + sqrt(3)` = 0,
then x = `-sqrt(3)`
or
`sqrt(3) x + 7` = 0,
then `sqrt(3)x` = –7
⇒ x = `(-7)/sqrt(3)`
x = `(-7 xx sqrt(3))/(sqrt(3) xx sqrt(3)`
= `(-7sqrt(3))/(3)`
Hence x = `-sqrt(3), (-7sqrt(3))/(3)`.
APPEARS IN
RELATED QUESTIONS
Let us find two natural numbers which differ by 3 and whose squares have the sum 117.
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
x2 – (m + 2)x + (m + 5) = 0
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.
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 + px + 3 = 0\]
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
In each of the following determine whether the given values are solutions of the equation or not.
3x2 - 2x - 1 = 0; x = 1
Solve the following equation by factorization
x(2x + 5) = 3
A two digit number contains the bigger at ten’s place. The product of the digits is 27 and the difference between two digits is 6. Find the number.
Solve the following quadratic equation by factorisation method:
x2 + x – 20 = 0
4x2 – 9 = 0 implies x is equal to ______.
