Question

Q3. Form a quadratic polynomial with 4 and -2 as the sum and product of its zeroes respectively1

Answer 1

Solution:

$Let \: \alpha\: and\: \beta \:be\: the \:zeros\: of \:required \: polynomial.$

Given,

$\alpha + \beta=4 \\ \\</p><p></p><p>and, \:\alpha\beta=-2$

To find:

Polynomial

Now,

Let the polynomial be f(x).

$f(x) = x {}^{2} - ( \alpha + \beta ) + \alpha \beta$

Putting the values,we get:

$f(x) = x {}^{2} - (4)x + ( - 2) \\ \: \: \: \: \: \: \: \: \: \: \: = x {}^{2} - 4x - 2$

Hence,x^2-4x-2 is the required polynomial