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Based on remainder theorem..zeroes of biquadratic equation are gievn..please help with atleast few steps

Based on remainder theorem..zeroes of biquadratic equation are gievn..please help with atleast few steps

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Grade:12

1 Answers

Aditya Gupta
2081 Points
4 years ago
 
dear student, biquadratic polynomial means it has degree 4.
also, since its roots are given to be – 2, 3, 5, 7, it means that we can factorise f(x) as follows:
f(x)= A(x – ( – 2))(x – 3)(x – 5)(x – 7)
= A(x+2)(x – 3)(x – 5)(x – 7), where A is the leading coefficient.
put x=0 both sides
f(0)= A(2)(-3)(-5)(-7)
or A= – 1/210, since f(0)= 1
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
KINDLY APPROVE :))

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