Question

the polynomial p(x) have -2 & 5 as zeroes. the polynomial p( x) is equal to. (a) x^2-3x+10
(b) x^2-3x-10
(c) x^2+3x+10
(d) none of the above​

Answer 1

Answer:

(b). x² - 3x - 10

Step-by-step explanation:

f (x) = ax² + bx + c , and $x_{1}$ and $x_{2}$ are zeros of f(x) , then

$x_{1}$ + $x_{2}$ = - $\frac{b}{a}$

$x_{1}$$x_{2}$ = $\frac{c}{a}$

~~~~~~~~~~

- 2 + 5 = 3 ⇒ b = - 3, a = 1

5(- 2) = - 10 ⇒ c = - 10, a = 1

f(x) = x² - 3x - 10

There is another way:

ax² + bx + c = a(x - $x_{1}$)(x - $x_{2}$)

(x + 2)(x - 5) = ...