Question

Find the quadratic polynomial for which the sum and the product of zeroes are √5 and 3/4​

Answer 1

Answer:

(x2-3/4x*√5)

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Answer 2

Given:

The sum and product of zeroes of a quadratic polynomial are √5 and 3/4 respectively.

To find:

The quadratic polynomial.

Solution:

As we know that a quadratic equation p(x) is given by:

${x}^{2} - (sum \: of \: the \: zeroes)x + (product \: of \: the \: zeroes) = 0$

Now,

as given, we have,

The sum of zeroes of a quadratic polynomial = √5

The product of zeroes of a quadratic polynomial = 3/4.

Hence, the quadratic polynomial p(x) is-

${x}^{2} - \sqrt{5}x + \frac{3}{4}$

This can be written as

$4 {x}^{2} - 4\sqrt{5} + 3$

Hence, the quadratic polynomial with √5 and 3/4 as the sum of zeroes and product of zeroes respectively is

$4 {x}^{2} - 4\sqrt{5} + 3$