Advertisements
Advertisements
प्रश्न
Write the discriminant of the following quadratic equations:
x2 - 2x + k = 0, k ∈ R
उत्तर
We have been given, x2 - 2x + k = 0
Now we also know that for an equation ax2 + bx + c = 0, the discriminant is given by the following equation:
D = b2 - 4ac
Now, according to the equation given to us, we have,a = 1, b = -2 and c = k.
Therefore, the discriminant is given as,
D = (-2)2 - 4(1)(k)
= 4 - 4k
Therefore, the discriminant of the equation is 4 - 4k.
APPEARS IN
संबंधित प्रश्न
Write the discriminant of the following quadratic equations:
x2 - x + 1 = 0
In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
x2 - 2x + 1 = 0
In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
`2x^2-2sqrt2x+1=0`
`2x^2-5sqrt2x+4=0`
`16x^2+2ax+1`
`2x^2+5sqrt3x+6=0`
Find the nature of roots of the following quadratic equations:
` 3x^2-2sqrt6x+2=0`
If a and b are distinct real numbers, show that the quadratic equations
`2(a^2+b^2)x^2+2(a+b)x+1=0` has no real roots.
Find the values of k for which the quadratic equation `(3k+1)x^2+2(k+1)x+1=0` has real and equal roots.
Find the values of k for which the given quadratic equation has real and distinct roots:
`kx^2+6x+1=0`
