Advertisements
Advertisements
प्रश्न
Solve the following quadratic equation using formula method only
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
Advertisements
उत्तर
`3"x"^2 +2 sqrt 5 "x" -5 = 0`
a = 3 ; b = `2 sqrt 5` ; c= -5
D = b2 - 4ac
= `(2 sqrt 5)^2` - 4 (3)(-5)
= 20 + 60
= 80
x = `(- "b" ± sqrt ("b"^2 - 4 "ac"))/(2a)`
x = `(-(2 sqrt 5) +- sqrt 80)/6`
x = `(-(2 sqrt 5) +- 4 sqrt 5)/6`
x = `(-(2 sqrt 5) +- 4 sqrt 5)/6`
x = `(-2 sqrt 5 + 4 sqrt 5)/6` , x = `(-2 sqrt 5 - 4 sqrt 5)/6`
x = `sqrt 5 / 3` , x = `- sqrt 5`
APPEARS IN
संबंधित प्रश्न
In the following determine the set of values of k for which the given quadratic equation has real roots:
4x2 - 3kx + 1 = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 2x + 1 = 0
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and -ax2 + bx + c = 0 has real roots.
Find the value of k for which the given equation has real roots:
kx2 - 6x - 2 = 0
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`
Which of the following equations has 2 as a root?
The roots of the quadratic equation `"x" + 1/"x" = 3`, x ≠ 0 are:
Find the roots of the quadratic equation by using the quadratic formula in the following:
5x2 + 13x + 8 = 0
Every quadratic equations has at most two roots.
If the quadratic equation kx2 + kx + 1 = 0 has real and distinct roots, the value of k is ______.
