Question

form the quadratic equation whose zeroes are -4/5 and 1/3​

Answer 1

Answer: 15x²+7x-4.

Given:

$\sf \alpha=-\dfrac{4}{5}$

$\sf \beta=-\dfrac{1}{3}$

To find:

$\sf The\:quadratic\:equation.$

Formula used:

$\boxed{\sf x^2-(\alpha+\beta)x+\alpha\beta=0}$

Explanation:

$\sf Sum\:of\:zeroes(\alpha+\beta)=-\dfrac{4}{5}+\dfrac{1}{3} =-\dfrac{7}{15}$

$\sf Product\:of\:zeroes(\alpha\beta)=-\dfrac{4}{5}\times\dfrac{1}{3} =-\dfrac{4}{15}$

$\sf Now,$

$\Rightarrow{\sf x^2-\bigg(-\dfrac{7}{15} \bigg)x+\bigg(-\dfrac{4}{15}\bigg)=0$

$\Rightarrow{\sf x^2-\bigg(-\dfrac{7x}{15} \bigg)-\dfrac{4}{15}=0$

$\Rightarrow{\sf15x^2+{7x}-\dfrac{4}{15}=0$

$\Rightarrow\boxed{\sf15x^2+7x-4=0}$

Therefore, the quadratic equation is 15x²+7x-4.