Please help with the 78th question of biquadratic equations..
Neelakantan , 4 Years ago
Grade 12
Algebra> Please help with the 78th question of biq...
1 Answers
Aditya Gupta
Last Activity: 4 Years ago
dear student, biquad polynomial means it has degree 4.
also, since its roots are given to be – 2, 3, 5, 7, it means that we can write f(x) as follows:
f(x)= A(x – ( – 2))(x – 3)(x – 5)(x – 7)
= A(x+2)(x – 3)(x – 5)(x – 7)
put x=0 both sides
f(0)= A(2)(-3)(-5)(-7)
or A= – 1/210
so, the remainder when f(x) is divided by x – 1, would be f(1) (using remainder theorem)
so, f(1)= A(1+2)(1 – 3)(1 – 5)(1 – 7)
= – (1/210)(3)(-2)(-4)(-6)
= 24/35
option C
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