Find a quadratic polynomial, the sum and product of whose zeroes are $0$ and $-\frac{3}{5}$ respectively. Hence find the zeroes.

Given: The sum and product of zeroes of a quadratic polynomial $0$ and $-\frac{3}{5}$ respectively.

To do: To write the polynomial. And to find its zeroes.

Solution:

Let $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial.

As given $\alpha+\beta=0$ and $\alpha\beta=-\frac{3}{5}$

The polynomial is:

$x^2-( \alpha+\beta)x+\alpha\beta=0$

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

$\Rightarrow x^2-\frac{3}{5}=0$

$\Rightarrow 5x^2-3=0$

$\Rightarrow x^2=\frac{3}{5}$

$\Rightarrow x=\pm\sqrt{\frac{3}{5}}$

Thus the polynomial is $5x^2-3=0$ and the the zeroes are $x=\sqrt{\frac{3}{5}},\ -\sqrt{\frac{3}{5}}$.

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Updated on: 10-Oct-2022

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