Question

How to find alpha square minus beta square for same quadratic polynomial x^2-5x+6

Answer 1

Answer :

The given quadratic polynomial is f(x) = x² - 5x + 6

We need to find ( α² - β² ), where α and β be the roots of the equation f(x) = 0. So, we factorize it.

Now, x² - 5x + 6

    = x² - 3x - 2x + 6

    = x ( x - 3 ) - 2 ( x - 3 )

    = ( x - 3 ) ( x - 2 )

Since ( x - 3 ) and ( x - 2 ) are the factors of f(x), 3 and 2 be the roots of f(x) = 0, and we consider either α or β having values 3 and 2 correspondingly.

Now, α² - β² = 3² - 2² = 9 - 4 = 5

or, α² -β² = 2² - 3² = 4 - 9 = - 5

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