if alpha and beta are the two zroes of quadratic polynomial f(x)=x2-px+q then find the value of alpha square-beta square
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f(x) = x² - px + q
Let alpha = à and beta = ß
à and ß are zeroes.
Sum of zeroes = -x coefficient/x² coefficient
à+ß = -(-p)/1 = p
Product of zeroes = constant/x² coefficient
àß = q/1 = q
(à-ß)² = (à+ß)² - 4àß
(à-ß)² = p² - 4q
(à-ß) = √p²-4q
ಠ- ß² = (à+ß) (à-ß)
= p(√p²-4q)
(If you want to find ಠ+ ߲,then follow the process::
à²+ß² = (à+ß)² - 2àß
= p²-2q)
Let alpha = à and beta = ß
à and ß are zeroes.
Sum of zeroes = -x coefficient/x² coefficient
à+ß = -(-p)/1 = p
Product of zeroes = constant/x² coefficient
àß = q/1 = q
(à-ß)² = (à+ß)² - 4àß
(à-ß)² = p² - 4q
(à-ß) = √p²-4q
ಠ- ß² = (à+ß) (à-ß)
= p(√p²-4q)
(If you want to find ಠ+ ߲,then follow the process::
à²+ß² = (à+ß)² - 2àß
= p²-2q)
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