Question

13. Use the factor theorem to determine whether g(x)
is a factor of f(x) or not.
(i) f(x) = x3 + x2 – 10x + 8; g(x) = x + 4
(ii) f(x) = x3 – 7x - 6; g(x) = x - 3
(iii) f(x) = 2x3 - 3x3 - 5x; g(x) = x + 1
(iv) f(x) = 2562 – 2/2x2 + 12x + 4; g(x) = x – V2​

Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.

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