Question

find the quadratic polynomial whose sum and product of the zeroes are 21/8 and 5/16 respectively

Answer 1

When two roots of a quadratic polynomial are a and b, then the quadratic formed is (x-a)(x-b).
If you expand this, it becomes

x²-(a+b)x+ab

You can see here,that the coefficient of x is the negative of sum of roots and the constant is the product of roots.

Hence you simply need to replace the values, like done in the other answer.

The quadratic becomes,

x²-(21/8)x+5/16

Answer 2

Answer:

The required quadratic polynomial is $16x^2-42x+5$

Step-by-step explanation:

Given : The quadratic polynomial whose sum and product of the zeroes are 21/8 and 5/16 respectively.

To find : The quadratic polynomial?

Solution :

The quadratic polynomial sum of the zeroes is

$\alpha+\beta=\frac{21}{8}$

The quadratic polynomial product of the zeroes is

$\alpha\beta=\frac{5}{16}$

The required form of the quadratic polynomial is

$k(x^2-(\alpha+\beta)x+\alpha \beta )$

Substituting the values,

$k(x^2-(\frac{21}{8})x+\frac{5}{16})$

$k(x^2-(\frac{42}{16})x+\frac{5}{16})$

Here, The value of k=16

$16(x^2-(\frac{42}{16})x+\frac{5}{16})$

$16x^2-42x+5$

Therefore, The required quadratic polynomial is $16x^2-42x+5$