Advertisements
Advertisements
Question
Solve the following equation by factorization
`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0
Solution
`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0
`{4sqrt(3) xx (-2sqrt(3)) = 8xx (-3) = -24}`
`4sqrt(3)x^2 + 8x - 3x - 2sqrt(3)` = 0
⇒ `4x (sqrt(3)x + 2) - sqrt(3)(sqrt(3)x + 2)` = 0
⇒ `(sqrt(3)x + 2) (4x - sqrt(3))` = 0
Either `sqrt(3)x + 2` = 0,
then `sqrt(3)x` = -2
⇒ x = `-(2)/sqrt(3)`
⇒ x = `(-2 xx sqrt(3))/(sqrt(3) xx sqrt(3))`
= `(-2sqrt(3))/(3)`
or
`4x - sqrt(3)` = 0,
then `4x = sqrt(3)`
⇒ x = `sqrt(3)/(4)`
Hence x = `(-2sqrt(3))/(3), sqrt(3)/(4)`.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
`(x+3)/(x-2)-(1-x)/x=17/4`
The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
Solve 2x2 – 9x + 10 =0; when x ∈ Q
The sum of the squares two consecutive multiples of 7 is 1225. Find the multiples.
Solve the following quadratic equation by factorisation.
\[25 m^2 = 9\]
Factorise : m2 + 5m + 6.
The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
Solve the following equation by factorization
x2 – (p + q)x + pq = 0
Two squares have sides A cm and (x + 4) cm. The sum of their areas is 656 sq. cm.Express this as an algebraic equation and solve it to find the sides of the squares.
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
