Question

form the quadratic equation whose zeroes are 3 and 1/5 step by step explanation ​

Answer 1

Answer:

$5 {x}^{2} - 16x + 3 = 0$

Explanation:

Let the zeroes be

$\alpha = 3$

$\beta = \frac{1}{5}$

A quadratic equation whose roots are α,β is

$k( {x}^{2} - ( \alpha + \beta )x + \alpha \beta )$

where k is any real number.

Putting the values we get

$k( {x}^{2} - (3 + \frac{1}{5} )x + (3 \times \frac{1}{5} ))$

$k( {x}^{2} - \frac{16}{5} x + \frac{3}{5} )$

$\frac{k}{5} (5 {x}^{2} - 16x + 3)$

Putting k=5, we get the quadratic equation

$5 {x}^{2} - 16x + 3$