Advertisements
Advertisements
प्रश्न
Find the nonzero value of k for which the roots of the quadratic equation `9x^2-3kx+k=0` are real and equal.
उत्तर
The given equation is `9x^2-3kx+k=0`
This is of the form `ax^2+bx+c=0,` where `a=9, b=-3k and c=k`
∴ `D=b^2-4ac=(-3k)^2-4xx9xxk=9k^2-36k`
The given equation will have real and equal roots if D = 0.
∴` 9k^2-36k=0`
⇒` 9k(k-4)=0`
⇒ `k=0 or k-4=0`
⇒`k=0 or k=4`
But, k ≠ 0 (Given)
Hence, the required values of k is 4.
APPEARS IN
संबंधित प्रश्न
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:
`sqrt3x^2+10x-8sqrt3=0`
Solve for x:
`1/x - 1/(x-2)=3`, x ≠ 0, 2
`x^2-6x+4=0`
`3a^2x^2+8abx+4b^2=0`
`a^2b^2x^2-(4b^4-3a^4)x-12a^2b^2=0,a≠0 and b≠ 0`
Find the nature of roots of the following quadratic equations:
`5x^2-4x+1=0`
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.
If the quadratic equation x2 + 4x + k = 0 has real and equal roots, then ______.
