The equation connecting a and b in order that 2x4 - 7x3 + ax + b is divisible by x - 3 is exactly divisible a) 3a - 2b = 27 b) 3a - b = 27 c) 3a + b = 27 d) 3a + b = 20 Video Auto Play
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Find the value of a and b so the polynomial (x
4
+ax
3
−7x
2
−8x+b) exactly divisible by (x+2) as well (x+3).
Given : Polynomial x
4
+ax
3
−7x
2
−8x+b is exactly divisible
by (x+2) as well (x+3)
⇒x=−2,−3 are the roots of polynomial
∴(−2)
4
+a(−2)
3
−7(−2)
2
−8(−2)+b=0
16−8a−28+16+b=0
−8a+b=−4 ... (I)
(−3)
4
+a(−3)
3
−7(−3)
2
−8(−3)+b=0
81−27a−63+24+b=0
−27+b=−42 .... (II)
(I) - (II)
Ref. Image
a=2
put a=2 in equation (I)
−16+b=−4
b=−4+16
b=12
∴a=2,b=12
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