Check the solution to "If b is the largest zero of x3−5x2−x+5..."

Prince Rasmussen

Answered question

2022-02-05

If b is the largest zero of

x^{3} - 5 x^{2} - x + 5

then which of the following quadratic equations is it also a zero of?
1)

x^{2} - 3 x - 10 = 0

x^{2} + 3 x - 10 = 0

x^{2} - 3 x + 10 = 0

x^{2} + 3 x + 10 = 0

Utskoldendv3

Beginner2022-02-06Added 9 answers

First factor

x^{3} - 5 x^{2} - x + 5

by grouping to find its zeros:

x^{3} - 5 x^{2} - x + 5

= (x^{3} - 5 x^{2}) - (x - 5)

= x^{2} (x - 5) - 1 (x - 5)

= (x^{2} - 1) (x - 5)

= (x - 1) (x + 1) (x - 5)

which has zeros:

1, - 1.5

b = 5

Substituting this value of b for x in 1), we find:

x^{2} - 3 x - 10 = 5^{2} - (3 \cdot 5) - 10 = 25 - 15 - 10 = 0

So the answer 1)

x^{2} - 3 x - 10 = 0

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