If -2 is root of eqyation 3x²+7x+p=0 find the value of k show that the root of equation x²+k(4x+k-1)+p=0 are equal
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Step-by-step explanation:
Let f(x)=3x²+7x+p
Since -2 is a root of f(x),
f(-2)=0
3(-2)²+7(-2)+p=0
12-14+p=0
P=2
F(x)=3x²+7x+p
X²+k(4x+k—1)+2=0
X²+4kx+k²—k+2=0
∆=16k²—4(k²—k+2)
=16k²—4k²+4k—8
=12k²+4k—8
Two have equal roots
∆=0
12k²+4k—8=0
3k²+k—2=0
3k²+3k—2k—2=0
3k(k+1)—2(k+1)=0
(3k—2)(k+1)=0
K=2/3, k=-1
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