If alpha and beta are the zeroes of the quadratic polynomial f(x)=x^{2-px+q then find the values of (1)alpha}2 + beta²

Open in App

Solution

We know (a+b)² = a² + b² + 2ab

So a² + b² = (a+b)² - 2ab

Similarly α² + β² = (α+β)² - 2αβ

Put value of (α+β) and αβ we will get

α² + β² = (α+β)² - 2αβ

α² + β² = p² - 2q

Answer : α² + β² = p² - 2q

Suggest Corrections

Similar questions

If alpha and beta are zeroes of the quadratic polynomial x2-5x+4, then find all the quadratic polynomials whose zeroes are alpha+1/beta and beta+1/alpha.

Join BYJU'S Learning Program

If alpha and beta are the zeroes of the quadratic polynomial f(x)=x2-px+q then find the values of (1)alpha2 + beta2

We know (a+b)² = a² + b² + 2ab So a² + b² = (a+b)² - 2ab Similarly α² + β² = (α+β)² - 2αβ Put value of (α+β) and αβ we will get α² + β² = (α+β)² - 2αβ α² + β² = p² - 2q Answer : α² + β² = p² - 2q

If alpha and beta are the zeroes of the quadratic polynomial f(x)=x^{2-px+q then find the values of (1)alpha}2 + beta²

We know (a+b)² = a² + b² + 2ab

So a² + b² = (a+b)² - 2ab

Similarly α² + β² = (α+β)² - 2αβ

Put value of (α+β) and αβ we will get

α² + β² = (α+β)² - 2αβ

α² + β² = p² - 2q

Answer : α² + β² = p² - 2q