Advertisements
Advertisements
प्रश्न
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
उत्तर
`2"x"^2- 2 sqrt 6 + 3 = 0`
a = 2 ; b = `- 2 sqrt 6 "x"` ; c = 3
D = b2 - 4ac
= (- 2 sqrt 6)2 - 4(2)(3)
= 12 - 24
= -12
x = `(- "b" ± sqrt ("b"^2 - 4 "ac"))/(2a)`
x = `(2 sqrt 6 +- sqrt -12)/2`
x = `(2 sqrt 6)/4`
x = `sqrt 6/2`
APPEARS IN
संबंधित प्रश्न
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Determine the nature of the roots of the following quadratic equation :
x2 +3x+1=0
Determine the nature of the roots of the following quadratic equation :
2x2 + 5x - 6 = 0
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
Find, using the quadratic formula, the roots of the following quadratic equations, if they exist
3x2 – 5x + 2 = 0
Find the nature of the roots of the following quadratic equations: `x^2 - (1)/(2)x - (1)/(2)` = 0
The equation 12x2 + 4kx + 3 = 0 has real and equal roots, if:
If α and β be the roots of the equation x2 – 2x + 2 = 0, then the least value of n for which `(α/β)^n` = 1 is ______.
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
