if a = 23 x square - 4 x + 1, then equal to 5 x square + 3 x minus 8 and C is equal to 4 x square - 7 x + 3 then find b + c minus A
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Answer:
Given x=−2 is root of equation 3x
2
+7x+p=0
∴x=−2 satisfies the given equation
3(−2)
2
+7(−2)+P=0
12+(−14)+P=0
P=2
The given equation becomes 3x
2
+7x+2=0
3x
2
+6x+x+2=0
3x(x+2)+1(x+2)=0
(3x+1)(x+2)=0
x=
3
−1
or x=−2
Now, x
2
+K(4x+k−1)+P=0
roots are equal
∴D=0D=b
2
−4ac
x
2
+4xk+k
2
−k+2=0
a=1 b=4k C=k
2
−k+2=0
(4k)
2
−4(k
2
−k+2)=0
16k
2
−4k
2
+4k−8=0
12k
2
+4k−8=0
12k
2
+12k−8k−8=0
2k(k+1)−8(k+1)=0
k=
12
8
=
3
2
k=−1.
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