Question

If alpha and beta are the zeros of the quadratic polynomials f (x) =x2-px+q, find the value of Alpha square + beta square

Answer 1

Heya Dear,

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Given,

 α and ß are the zeroes of polynomial x² - px + q.

In this quadratic equation,

Coefficient of x² ( a ) = 1

Coefficient of x( b ) = -p

Constant term ( c ) = q.

We have,

⇒ Sum of zeroes = -b/a

⇒ α + ß = - ( - p ) / 1

∴ α + ß = p.

⇒ Product of zeroes = c/a

⇒ αß = q/1 = q

Now,

⇒ ( α + ß )² = α² + ß² + 2 αß

⇒ ( p )² = α² + ß² + 2 q

⇒ p² = α² + ß² + 2 q

∴ α² + ß² = p² - 2q


Hope it helps !

Answer 2

See the attachement for calculation

[α²+β²]=[p²-2q]

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