Answer: x-intercepts (5,0), (2,0), (1,0)
y-intercept (0,-10)
Step-by-step explanation: If one factor of the polynomial function is (x-5), then the function f(x) can be factored in the following way: (x-5) (x^2-3x+2)
Now factor the trinomial: (x-2) (x-1)
Thus, x-intercepts (points where f(x)=0) are
x1=5
x2=2
x3=1
and y-intercept (point where x=0) is
f(0)=0^3-8.0^2+17.0-10=-10.
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A function assigns the values. The y-intercept of the function is -10, while the x-intercept of the function is 5, 2, and 1.
A function assigns the value of each element of one set to the other specific element of another set.
To find an intercept of the function, we need to substitute the value of x or y depending on the intercept as 0 in the function. Therefore, the x-intercept of the function is,
y = (0)³ - 8(0)² + 17(0) - 10
y = -10
Since given that one factor of the function f(x)=x³-8x²+17x-10 is (x-5). Therefore, if the function f(x) is divided by (x-5). The quotient will be x²-3x+2.
Now, Factorising the given expression x²-3x+2.
x²-3x+2
= x² - 2x - x + 2
= x(x-2) -1(x-2)
= (x-2)(x-1)
Now, we can write the function f(x)=x³-8x²+17x-10 as y=(x-5)(x-2)(x-1). Therefore, the x-intercept of the function is,
x-intercept = 5, 2, 1
This can be verified from the graph formed below.
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