Ife& β are the zeros of the quadratic polynomial p(x) = x2 + 7x + 12

1.	Ife& β are the zeros of the quadratic polynomial p(x) = x2 + 7x + 12, find thevalue ofi) \alpha^{2} \beta+\alpha \beta^{2} \quad \text { ii) } \alpha^{2}+\beta^{2}
Answer» Sum of zeroes, α + β = -7 andProduct of zeroes, αβ=12 i) α²β + αβ²= (α + β)αβ= -84 ii) α² + β² =( α+β)²-2αβ= 49-24=25

Ife& β are the zeros of the quadratic polynomial p(x) = x2 + 7x + 12, find thevalue ofi) \alpha^{2} \beta+\alpha \beta^{2} \quad \text { ii) } \alpha^{2}+\beta^{2}

Answer»

Sum of zeroes, α + β = -7 andProduct of zeroes, αβ=12

i) α²β + αβ²= (α + β)αβ= -84

ii) α² + β² =( α+β)²-2αβ= 49-24=25