Advertisements
Advertisements
प्रश्न
Write the discriminant of the following quadratic equations:
(x − 1) (2x − 1) = 0
उत्तर
We have been given, (x − 1) (2x − 1) = 0
Now, simplify the equation to be represented in the quadratic form, so we have
2x2 - x - 2x + 1 = 0
2x2 - 3x + 1 = 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 = 2, b = -3 and c = 1.
Therefore, the discriminant is given as,
D = (-3)2 - 4(2)(1)
= 9 - 8
= 1
Therefore, the discriminant of the equation is 1.
APPEARS IN
संबंधित प्रश्न
Write the discriminant of the following quadratic equations:
3x2 + 2x + k = 0
In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
`3x^2+2sqrt5x-5=0`
In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
`2x^2+5sqrt3x+6=0`
`3x^2-243=0`
`sqrt3x^2+10x-8sqrt3=0`
`x+1/x=3,x≠0`
`x^2-2ax+(a^2-b^2)=0`
`4x^2-4bx-(a^2-b^2)=0`
Find the nature of roots of the following quadratic equations:
`5x^2-4x+1=0`
Find the value of p for which the quadratic equation `(2p+1)x^2-(7p+2)x+(7p-3)=0` has real and equal roots.
