Question

Form a quadratic equation whose sum and product of the zeroes are √3 and -1/2

Answer 1

Here

We have to form an equation whose :

Sum of zeroes : √3

Product of zeroes : -½

Solution :

By using the formulae :

k[x²-(sum of zeroes)x+Product of zeroes)]

For full solution refer to the above attachment.

Answer 2

$let \: the \: zeros be \: \alpha and \: \beta$

According to question ,

$\alpha + \beta = \sqrt{3}$

$\alpha \beta = - 1 \div 2$

Let the required polynomial be p(x).

Since ,

a quadratic polynomial with zeros alpha and beta is given by

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

Thus ,p(x)=

k(x2-√3x-1/2)

→p(x)= 2x^2 -2√3x -1 [Take , k=2as constant ]