Advertisements
Advertisements
प्रश्न
For what values of k are the roots of the quadratic equation `3x^2+2kx+27` real and equal ?
उत्तर
Given:
`3x^2+2kx+27=0`
Here,
`a =3,b=2k and c=27`
It is given that the roots of the equation are real and equal; therefore, we have:
`D=0`
⇒`(2k)^2-4xx3xx27=0`
⇒`4k^2-324=0`
⇒`4k^2=324`
⇒`k^2=81`
⇒ `k=+-9`
∴ `k=9 or k=-9`
APPEARS IN
संबंधित प्रश्न
In the following, determine whether the given quadratic equation have real roots and if so, find the roots:
x2 + x + 2 = 0
`2x^2+x-4=0`
`sqrt3x^2-2sqrt2x-2sqrt3=0`
`x^2-2ax-(4b^2-a^2)=0`
`x^2+6x-(a^2+2a-8)=0`
For what values of p are the roots of the equation `4x^2+px+3=0` real and equal?
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.
If 3 is a root of the quadratic equation` x^2-x+k=0` find the value of p so that the roots of the equation `x^2+2kx+(k^2+2k+p)=0` are equal.
Find the value of k for which the roots of `9x^2+8kx+16=0` are real and equal
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.
