x2 + (p - 1)x + (p + 2) = 0
find the value of p without solving
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Answer:
From equation (i),
px
2
−4x+3=0
a=p,b=−4 and c=3
If the roots of this equation are equal and real, then D=0.
Therefore,
D=b
2
−4ac=0
(−4)
2
−4×p×3=0
16−12p=0
12p=16
p=
3
4
So, the value of p is
3
4
.
From equation (ii),
x
2
+(p−3)x+p=0
a=1,b=(p−3) and c=p
If the roots of this equation are equal and real, then D=0.
Therefore,
D=b
2
−4ac=0
(p−3)
2
−4×1×p=0
p
2
+9−6p−4p=0
p
2
−10p+9=0
p
2
−9p−p+9=0
p(p−9)−1(p−9)=0
(p−1)(p−9)
p=1,9
So, the values of p is 1,9.
Hence, this is correct answer.
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