Advertisements
Advertisements
Question
Find the nature of roots of the following quadratic equations:
` 3x^2-2sqrt6x+2=0`
Solution
The given equation is `3x^2-2sqrt6x+2=0`
This is of the form `ax^2+bx+c=0` where `a=2, b=-8 and c=5`
∴ Discriminant, `D=b^2-4ac=(-2sqrt6)^2-4xx3xx2=24-24=0`
Hence, the given equation has real and equal roots.
APPEARS IN
RELATED QUESTIONS
Write the discriminant of the following quadratic equations:
2x2 - 5x + 3 = 0
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:
`2x^2-2sqrt2x+1=0`
Solve for x
`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`; x ≠ 2, 4
`3x^2-243=0`
`3/n x^2 n/m=1-2x`
`3a^2x^2+8abx+4b^2=0`
Find the values of k for which the given quadratic equation has real and distinct roots:
`9x^2+3kx+4=0`
Find the value of a for which the equation `(α-12)x^2+2(α-12)x+2=0` has equal roots.
The denominator of a fraction is 3 more than its numerator. The sum of the fraction and its reciprocal is `2 9/10` Find the fraction.
