Advertisements
Advertisements
प्रश्न
`4x^2+4sqrt3x+3=0`
Advertisements
उत्तर
`4x^2+4sqrt3x+3=0`
⇒` 4x^2+4sqrt3x=-3`
⇒`(2x)^2+2xx2x xxsqrt3+(sqrt3)^2=-3(sqrt3)^2` [Adding`( sqrt3)^2` on both sides]
⇒`(2x+sqrt3)^2=-3+3=0`
⇒`2x+sqrt3=0`
⇒`x=-sqrt3/2`
Hence,`-sqrt3/2` is the repeated root of the given equation.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations
(i) x2 + 5x = 0 (ii) x2 = 3x (iii) x2 = 4
Solve for x : 12abx2 – (9a2 – 8b2 ) x – 6ab = 0
Find the roots of the following quadratic equation by factorisation:
x2 – 3x – 10 = 0
Solve the following quadratic equations by factorization:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.
Two pipes running together can fill a tank in `11 1/9` minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
A dealer sells an article for Rs. 24 and gains as much percent as the cost price of the article. Find the cost price of the article.
The sum of the squares of two consecutive positive integers is 365. Find the integers.
Solve the following quadratic equations by factorization:
\[\frac{4}{x} - 3 = \frac{5}{2x + 3}, x \neq 0, - \frac{3}{2}\]
Write the sum of real roots of the equation x2 + |x| − 6 = 0.
Solve the following equation: `10"x" - 1/"x" = 3`
Solve the following equation:
`("x" + 1)/("x" - 1) - ("x" - 1)/("x" + 1) = 5/6 , "x" ≠ -1,1`
Solve the following equation: `"a"("x"^2 + 1) - x("a"^2 + 1) = 0`
Some students planned a picnic. The budget for the food was Rs. 480. As eight of them failed to join the party, the cost of the food for each member increased by Rs. 10. Find how many students went for the picnic.
In each of the following determine whether the given values are solutions of the equation or not
2x2 - 6x + 3 = 0; x = `(1)/(2)`
Solve the following equation by factorization
3(x – 2)2 = 147
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
Two pipes running together can fill a tank in `11(1)/(9)` minutes. If one pipe takes 5 minutes more than the other to fill the tank, find the time in which each pipe would/fill the tank.
