Question

Find a quadratic equation each with the given numbers as the sum and product of its zeroes respectively.

$\frac{-2\sqrt{5}}{3},-\frac{5}{3}$

• A. $3x^2+4\sqrt{5}x-5=0$
• B. $3x^2+2\sqrt{5}x-5=0$
• C. $3x^2+3\sqrt{5}x-5=0$
• D. $3x^2+7\sqrt{5}x-5=0$

Answer 1

Answer: (B)

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

Given,
Sum of the roots=$\frac{-2\sqrt{5}}{3}$

Product of the roots $=-\frac{5}{3}$

Now, the quadratic equation is given by,

$x^2-$(sum of roots)$x+$(product of the roots) $=0$

$x^2-\left(\frac{-2\sqrt{5}}{3}\right)x+(-\frac{5}{3})=0$

$\frac{1}{3}(3x^2+2\sqrt{5}x-5)=0$

$\therefore 3x^2+2\sqrt{5}x-5=0$

The above equation is the required quadratic equation.