Advertisements
Advertisements
Question
Solve the following equation by using formula :
`sqrt(3)x^2 + 10x - 8sqrt(3)` = 0
Solution
`sqrt(3)x^2 + 10x - 8sqrt(3)` = 0
Here `a = sqrt(3), b = 10, c = -8sqrt(3)`
D = b2 - 4ac
= `(10)^2 - 4 xx sqrt(3) xx (-8sqrt(3))`
= 100 + 96
= 196
∵ x = `(-b ± sqrt("D"))/(2a)`
= `(-10 ± sqrt(196))/(2 xx sqrt(3))`
= `(-10 ± 14)/(2sqrt(3)`
∴ x1 = `(-10 + 14)/(2sqrt(3)`
= `(4)/(2sqrt(3)`
= `(2 xx sqrt(3))/(sqrt(3) xx sqrt(3)`
= `(2sqrt(3))/(3)`
x2 = `(-10 - 14)/(2sqrt(3)`
= `(-24)/(2sqrt(3)`
= `(-12 xx sqrt(3))/(sqrt(3) xx sqrt(3)`
= `(-12sqrt(3))/(3)`
= `-4sqrt(3)`
Hence x = `(2sqrt(3))/(3), -4sqrt(3)`.
APPEARS IN
RELATED QUESTIONS
Rs. 7500 were divided equally among a certain number of children. Had there been 20 less children, each would have received Rs. 100 more. Find the original number of children.
Solve the following equation and calculate the answer correct to two decimal places:
x2 – 5x – 10 = 0.
Check whether the following is quadratic equation or not.
x2 - 3x = 0
Check whether the following is quadratic equation or not.
(2𝑥 + 1)(3𝑥 + 2) = 6(𝑥 − 1)(𝑥 − 2)
Find the value of x, if a + 1=0 and x2 + ax – 6 =0.
Solve the following equation for x and give, in the following case, your answer correct to 3 decimal places:
2x2 + 11x + 4 = 0
`x/(x-1)+x-1/4=4 1/4, x≠ 0,1`
`a/(x-b)+b/(x-a)=2,x≠b,a`
If m and n are roots of the equation `1/x - 1/(x - 2) = 3`; where x ≠ 0 and x ≠ 2; find m × n.
Solve the following equation by using formula :
(2x + 3)(3x – 2) + 2 = 0
