Advertisements
Advertisements
प्रश्न
Solve the following equation by factorization
`4sqrt(3)x^2 + 5x - 2sqrt(3)` = 0
Advertisements
उत्तर
`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
संबंधित प्रश्न
Solve for x :
`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`
Solve (i) x2 + 3x – 18 = 0
(ii) (x – 4) (5x + 2) = 0
(iii) 2x2 + ax – a2 = 0; where ‘a’ is a real number
Solve the following quadratic equations by factorization:
`2/2^2-5/x+2=0`
Solve the following quadratic equations by factorization:
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1
Find the consecutive numbers whose squares have the sum 85.
The sum of a number and its square is 63/4. Find the numbers.
In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]
If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 cm2. However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm2. Determine the sides of the two squares.
Solve the quadratic equation: x2 – 2ax + (a2 – b2) = 0 for x.
If α and β are roots of the quadratic equation x2 – 7x + 10 = 0, find the quadratic equation whose roots are α2 and β2.
