Question

Find a quadratic polynomial, the stun and product of whose zeroes are √3 and 1√3 respectively.

Answer 1

Answer:

• √3x² - 3x + 1 = 0

Step-by-step explanation:

From the given information in the question, we have following results relating to zeroes of quadratic equation:

• Sum of zeroes = √3
• Product of zeroes = 1/√3

We are asked to find the quadratic equation.

In general, for any quadratic equation, whose zeroes are a and b, the equation is given by:

$\sf \implies x^2 - (a+b)x + ab = 0$

We have the value of sum and product of zeroes. By substituting the values, we get:

$\sf \implies x^2 - \sqrt{3}x + \dfrac{1}{ \sqrt{3} } = 0$

Multiplying the equation with √3 will give us:

$\sf \implies \underline{\sqrt{3} x^2 - 3 x + 1 = 0 }$

This is the required quadratic equation.