Write a polynomial function of least degree with rational coefficients so that P(x)0 has the given roots. x=-5, x=10
1 answer:
Answer:
P(x) = x² - 15x + 50
Step-by-step explanation:
We write the polynomial function P(x), given that P(x) = 0 has the given roots, x = 5 and x = 10.
Since x = 5 and x = 10 are the roots of P(x) = 0, it follows that (x - 5) and (x - 10) are factors of P(x) = 0. So, P(x) = (x -5)(x - 10) = 0
Expanding the brackets, we have
x² - 10x - 5x + 50 = 0
Simplifying, we have
x² - 15x + 50 = 0 = P(x)
Thus,
P(x) = x² - 15x + 50
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