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If alpha and beta are the zeros of the quadratic polynomial f(x)=x^2-px+q then find (i)alpha square +beta square (ii)1÷alpha+1÷beta

Posted by Prakrathi Hebri 5 years, 1 month ago

CBSE > Class 10 > Mathematics

2 answers

Prakrathi Hebri 5 years, 1 month ago

0Thank You

Gaurav Seth 5 years, 1 month ago

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

2Thank You

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