Question

Write a quadratic polynomial, sum of whose zeroes is 2√3 and product is 5.​

Answer 1

Answer:

A quadratic polynomial whose sum and product of zeroes are given can be written as -

${x}^{2} - sumx + product$

So in this question we can write the quadratic equation as -

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

Hope it helps..!!☺

Answer 2

Thus, the quadratic polynomial is ${x}^{2} - 2 \sqrt{3} x + 5 = 0$.

Given:

The sum of zeros of a quadratic equation is 2√3 and the product is 5.

To find:

The quadratic polynomial.

Let the quadratic polynomial is

$a {x}^{2} + bx + c = 0$

The sum of zeros of a quadratic equation is 2√3 and the product is 5.

Thus we can write-

$\frac{ - b}{a} = 2 \sqrt{3} \\ \frac{c}{a} = 5 \\ b = - 2 \sqrt{3} a \\ c = 5a$

Putting the value in the above expression we get-

$a {x}^{2} + bx + c = 0 \\ a {x}^{2} - 2 \sqrt{3}a + 5a = 0 \\ {x}^{2} - 2 \sqrt{3} x + 5 = 0$

Thus, the quadratic polynomial is ${x}^{2} - 2 \sqrt{3} x + 5 = 0$.

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