Advertisements
Advertisements
प्रश्न
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3) = 0`
Advertisements
उत्तर
`2sqrt(3)x^2 - 2sqrt(2)x - sqrt(3)` = 0.
Here, `a = 2sqrt(3), b = -2sqrt(2) and c = -sqrt(3)`
D = b2 - 4ac
⇒ D - 8 - 4 x 2`sqrt(3) xx- sqrt(3)`
⇒ D = 8 + 24
= 32 > 0
The given equation has real roots.
संबंधित प्रश्न
For what value of m, are the roots of the equation (3m + 1)x2 + (11 + m) x + 9 = 0 equal?
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 + 2(k + 3)x + (k + 8) = 0
Determine the nature of the roots of the following quadratic equation :
x2 -4x + 4=0
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
kx2 + 6x - 3k = 0, k ≠ 0
Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.
The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
If α and β are the distinct roots of the equation `x^2 + (3)^(1/4)x + 3^(1/2)` = 0, then the value of α96(α12 – 1) + β96(β12 – 1) is equal to ______.
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.
If x = 3 is one of the roots of the quadratic equation x2 – 2kx – 6 = 0, then the value of k is ______.
