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notsponge [240]
3 years ago
6

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

Mathematics
1 answer:
Ede4ka [16]3 years ago
8 0

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

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