Advertisements
Advertisements
प्रश्न
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.
उत्तर
It is given that 3 is a root of the quadratic equation `x^2-x+k=0`
∴ `(3)^2-3+k=0`
⇒ `k+6=0`
⇒ `k=-6`
The roots of the equation` x^2+2kx+(k^2+2k+p)=0 ` are equal.
∴ `D=0`
⇒`(2k)^2-4xx1xx(k^2+2k+p)=0`
⇒` 4k^2-4k^2-8k-4p=0`
⇒`-8k-4p`
⇒`p=(8k)/-4=-2k`
⇒ p=`-2xx(-6)=12`
Hence, the value of p is 12.
APPEARS IN
संबंधित प्रश्न
If the roots of the equation (a2 + b2) x2 – 2(ac + bd) x + (c2 + d2) = 0 are equal, prove that `a/b = c/d`
` 2x^2-7x+6=0`
`sqrt2x^2+7+5sqrt2=0`
`x^2+x+2=0`
`2x^2+5sqrt3x+6=0`
Find the nature of roots of the following quadratic equations:
`2x^2-8x+5=0`
Find the nonzero value of k for which the roots of the quadratic equation `9x^2-3kx+k=0` are real and equal.
If -5 is a root of the quadratic equation `2x^2+px-15=0` and the quadratic equation `p(x^2+x)+k=0` 0has equal roots, find the value of k.
Find the values of k for which the given quadratic equation has real and distinct root:
`5x^2-kx+1=0`
For what values of k, the roots of the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 are equal ?
