Question

If α,β are the zeros of the polynomial, x sq-px +36 and α sq + β sq = 9, then what is the value of p?​

Answer 1

Answer:

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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

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