Question

if x - 1 and x + 3 are factors of polynomial f(X) = x³ - hx² - 13x + k find values of h and k​

Answer 1

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Given→

f(x) = x³ - hx² - 13x + k

x-1 & x+3 are factors.

To find→

h & k

Solution→

We know that,

If x-a is a factor of p(x), then p(a)= 0.

Thus, p(1)= 0 & p(-3)=0

p(1)= 0

(1)³ - h(1)² - 13(1) + k = 0

1-h -13+k = 0

k - h -12 = 0

k- h = 12

k = 12 +h ---------(1)

p(-3) = 0

(-3)³ - h(-3)² - 13(-3) + k = 0

-27 - 9h +39+k= 0

k- 9h +12 = 0

12 +h -9h+12= 0 (from 1)

-8h = -24

h = 3

k = 12+3 (from 1)

k = 15