Question

verify that 1, -2and 1/2are zeros of 2x4+x2-5x+2. verify the relationship between the zeros and the coefficients

Answer 1

Answer:

Only 1, 1/2 are the zeros of the polynomial.

Step-by-step explanation:

Given : Equation - $f(x)=2x^4+x^2-5x+2$

To verify : 1, -2 and 1/2 are zeros of equation.

Solution : To verify whether they are zeros of polynomial or not we put the value of zeros in polynomial.

1) For x=1

$f(x)=2x^4+x^2-5x+2$

$f(1)=2(1)^4+1^2-5(1)+2$

$f(1)=0$

2) For x=-2

$f(x)=2x^4+x^2-5x+2$

$f(-2)=2(-2)^4+(-2)^2-5(-2)+2$

$f(-2)=38$

3) For x=1/2

$f(x)=2x^4+x^2-5x+2$

$f(-2)=2(\frac{1}{2})^4+(\frac{1}{2})^2-5(\frac{1}{2})+2$

$f(-2)=0$

Since only x=1 and x=1/2 verified that they are the zeros of the polynomial because by putting values f(x)

→The basic relationships between the zeros and the coefficients

$P(x)=ax^2+bx+c$ are

Sum of zeros = $\alpha+\beta=-\frac{b}{a}=-\frac{\text{coefficient of x}}{\text{coefficient of} x^2}$

Product of zeros = $\alpha\beta=\frac{c}{a}=\frac{\text{constant term}}{\text{coefficient of} x^2}$