If x2 + 3x – 10 is a factor of 3x4 + 2x3 – ax2 + bx – a + b – 4, then the closest approximate values of a and b are
Explanation:
x2 + 3x – 10 has 2 factors 2 and −5
x2 + 3x – 10 is a factor of 3x4 + 2x3 – ax2 + bx – a + b – 4
Therefore 2 and −5 are also the factors of this expression.
Substitute 2 and −5, to get 2 equations
For x = 2,
48 + 16 – 4a + 2b – a + b – 4 = 0
∴ 5a – 3b = 60…… (I)
For x = −5,
1875 – 250 – 25a – 5b – a + b – 4 = 0
26a + 4b = 1621……… (II)
Solving (I) and (II)
a = 52 and b = 67
Hence, option (c).
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