Question

Verify that the numbers given along side of the cubic polynomials below are their zeros. Also, verify the relationship between the zeros and coefficients in each case:

(i) $f\left(x\right)=2x^3+x^2-5x+2;\frac{1}{2},1,-2$
(ii) g(x) = x³ − 4x² + 5x − 2; 2, 1, 1

Answer 1

We have,

So, and are the zeros of polynomial p(x)

Let and . Then

From

Taking least common factor we get,

From

From

Hence, it is verified that the numbers given along side of the cubic polynomials are their zeros and also verified the relationship between the zeros and coefficients

(ii) We have,

So 2,1and 1 are the zeros of the polynomial g(x)

Let and. Then,

From

From

From

Hence, it is verified that the numbers given along side of the cubic polynomials are their

zeros and also verified the relationship between the zeros and coefficients.