Advertisements
Advertisements
प्रश्न
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 5x + 5 = 0
Advertisements
उत्तर
The given quadratic equation is
x2 + 5x + 5 = 0
Here, a = 1, b = 5 and c = 5
Discriminant
= b2 - 4ac
= (5)2 - 4 x 1 x 5
= 25 - 20
= 5 > 0
so the given equation has real roots given by
a = `(-b + sqrt(b^2 - 4ac))/(2a)`
= `(-5 + sqrt(25 - 4 xx 1 xx 5))/(2 xx 1)`
= `(-5 + sqrt(5))/(2)`
and β = `(-b - sqrt(b^2 - 4ac))/(2a)`
= `(-5 -sqrt(25 - 4 xx 1 xx 5))/(2 xx 1)`
= `(-5 - sqrt(5))/(2)`
संबंधित प्रश्न
If (k – 3), (2k + l) and (4k + 3) are three consecutive terms of an A.P., find the value of k.
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 3kx + 1 = 0
Find the values of k for which the roots are real and equal in the following equation:
kx(x – 2) + 6 = 0
Solve the following quadratic equation using formula method only
`sqrt 3 "x"^2 + 10 "x" - 8 sqrt 3 = 0`
Determine whether the given values of x is the solution of the given quadratic equation below:
6x2 - x - 2 = 0; x = `(2)/(3), -1`.
If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:
If –5 is a root of the quadratic equation 2x2 + px – 15 = 0, then:
If the difference of the roots of the equation x2 – bx + c = 0 is 1, then:
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, is ______.
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.
