Advertisements
Advertisements
प्रश्न
Solve the following quadratic equation using formula method only :
`2x + 5 sqrt 3x +6= 0 `
Advertisements
उत्तर
`2x + 5 sqrt 3x +6= 0 `
a = 2 ; b = `5 sqrt 3` ; c = 6
D = b2 - 4ac
D = `(5 sqrt 3)^2 - 4(2)(6)`
= 75 - 48
= 27
x = `(- "b" ± sqrt ("b"^2 - 4 "ac"))/(2a)`
x = `(-(5 sqrt 3) +- 3 sqrt 3)/4`
x = `(-(5 sqrt 3) + 3 sqrt 3)/4` , x = `(-(5 sqrt 3) - 3 sqrt 3)/4`
x = `(-2 sqrt 3)/4` , x = `(- 8 sqrt 3)/4`
x = `- sqrt 3/2` , x = `- 2 sqrt 3`
APPEARS IN
संबंधित प्रश्न
Find the value of k for which the roots are real and equal in the following equation:
3x2 − 5x + 2k = 0
The equation `3x^2 – 12x + (n – 5) = 0` has equal roots. Find the value of n.
Solve the following quadratic equation using formula method only
3x2 + 12 = 32 x
Find the values of k for which each of the following quadratic equation has equal roots: 9x2 + kx + 1 = 0 Also, find the roots for those values of k in each case.
Discuss the nature of the roots of the following equation: `sqrt(3)x^2 - 2x - sqrt(3)` = 0
If b2 – 4ac > 0 and b2 – 4ac < 0, then write the nature of roots of the quadratic equation for each given case.
If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
Solve the equation: 3x2 – 8x – 1 = 0 for x.
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, 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.
