If = −1, = 2 is a solution of the equation 3 + 4 + = 0 find the value of k.
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Answer:
(i) Let
p(x)=3x
2
+2kx−3
Given
−
2
1
is a solution of the equation p(x)=0,
∴p(−
2
1
)=0
⇒3(−
2
1
)
2
+2k(−
2
1
)−3=0
⇒
4
3
−k−3=0
⇒3−4k−12=0
⇒4k=−9
⇒k=−
4
9
(ii) Let
f(x)=7x
2
+kx−3
Given
−
3
2
is a solution of the equation f(x)=0,
∴f(
3
2
)=0
⇒7(
3
2
)
2
+k(
3
2
)−3=0
⇒
9
28
+
3
2k
−3=0
⇒28+6k−27=0
⇒6k=−1
⇒k=−
6
1
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