Question

The zeros of a polynomial are −1/2 and 3/7. Find the polynomial.

___x²+x− ___

Answer 1

Answer:

$y=14x^2+x-3$

Step-by-step explanation:

If the zeros of the polynomial are -1/2 and 3/7 then:

$\implies x=-\dfrac12$

Add 1/2 to both sides:

$\implies x+\dfrac12=0$

Multiply both sides by 2:

$\implies 2x+1=0$

$\implies x=\dfrac37$

Subtract 3/7 from both sides:

$\implies x-\dfrac37=0$

Multiply both sides by 7:

$\implies 7x-3=0$

Therefore, the factored form of the polynomial is $y=(2x+1)(7x-3)$

Expanding the brackets so that the polynomial is in standard form:

$\implies y=14x^2-6x+7x-3$

$\implies y=14x^2+x-3$