Advertisements
Advertisements
प्रश्न
Solve the following quadratic equation using formula method only
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
Advertisements
उत्तर
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
a = `sqrt 3` ; b = 10 ; c = `-8/sqrt 3`
D = b2 - 4ac
= `(10)^2 - 4 (sqrt 3) (-8 sqrt 3)`
= 100 + 96
= 196
x = `(- "b" ± sqrt ("b"^2 - 4 "ac"))/(2a)`
x = `(- 10 +- sqrt 196)/(2 sqrt 3)`
x = `(-10 + 14)/(2 sqrt 3)` , x = `(-10 - 14)/(2 sqrt 3)`
x = `4/(2 sqrt 3)` , x = `24/(2 sqrt 3)`
x = `2/sqrt 3` , x = `-12/ sqrt 3`
APPEARS IN
संबंधित प्रश्न
Without solving, examine the nature of roots of the equation x2 – 5x – 2 = 0
If the equation \[\left( 1 + m^2 \right) x^2 + 2 mcx + \left( c^2 - a^2 \right) = 0\] has equal roots, prove that c2 = a2(1 + m2).
Solve for x: (x2 - 5x)2 - 7(x2 - 5x) + 6 = 0; x ∈ R.
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
If b2 – 4ac > 0 and b2 – 4ac < 0, then write the nature of roots of the quadratic equation for each given case
The roots of quadratic equation 5x2 – 4x + 5 = 0 are:
If the quadratic equation ax2 + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.
The roots of the quadratic equation px2 – qx + r = 0 are real and equal if ______.
