Question

Find a formula for the product P of the solutions of the quadratic equation ax²+bx+c=0 .

Answer 1

Answer:

product of the roots= c/a

Step-by-step explanation:

The the two roots(α and β) of the quadratic equation ax²+bx+c=0  as given by shridharacharya formula are

$\alpha= \frac{-b+\sqrt{b^2-4ac} }{2a}$

$\beta= \frac{-b-\sqrt{b^2-4ac} }{2a}$

now product of the roots

αβ= $\frac{-b+\sqrt{b^2-4ac} }{2a}$×$\frac{-b-\sqrt{b^2-4ac} }{2a}$

use formula (a+b)(a-b)= a^2-b^2 and solve we get

αβ= c/a

therefore product of the roots= c/a