Question

If x=-2 is a root of the equation 3x²+7x+p=0, find the value of k so that the roots of the equation x²+k(4x+k-1)+p=0 are equal.
(Class 10 Maths Sample Question Paper)

Answer 1

Given:

x= - 2
3x² +7x +p =0
Put the value of eq x= -2 in above equation

3(-2)² +7(-2) +p =0
3 (4) -14 +p = 0
12 - 14 + p = 0
-2 +p = 0
p = 2

x² + k(4x +k -1) +p =0 ( given)
x² + 4kx + k² +k +2 = 0  (p = 2)

Root of the equation x² + 4kx +k² -k +2= 0 are equal.
Discriminant (D) = b² -4ac

Here a= 1, b= 4k, c = k² - k +2
D= (4k)² - 4(1× k²-k+2)
0 = 16k² - 4 (k²-k+2)
0= 16k² - 4k² + 4k - 8
0 = 12k² + 4k -8
0 = 4(3k² + k -2)
3k² + k -2= 0
3k² + 3k - 2k -2= 0

3k (k +1) - 2(k+1)= 0
(3k -2) (k+1) = 0
3k -2= 0
3k = 2

k = ⅔

k+1= 0
k = -1

Hence, the value of k= ⅔, -1

HOPE THIS WILL HELP YOU....

Answer 2

if a root is -2
3(-2)(-2)+7(-2)+p=0
p=2
eq 2=x.x+4.k.x+(k.k-k+p)=0    (put p=2)
 D(of second eq.)=b.b-4.a.c=0(as roots are equal)
[tex] (4k)^{2}=( k^{2}-k+2 )4 [/tex]$16 k^{2}=4 k^{2}-4k+8$$3 k^{2}+k-2=0$$(k+1)(3k-2)=0$$k=-1 or k=2/3$