Let P(x) be a quadratic polynomial such that P(0)P(0)P(1)P(2)=0. Let P(0)=2 and P(1)+P(2)+P(3)=14. Then P(4) equals

Question

Let P(x) be a quadratic polynomial such that ​P(0)P(0)​P(1)P(2)​​=0. Let P(0)=2 and P(1)+P(2)+P(3)=14. Then P(4) equals

Accepted Answer

Let P(x)=ax2+bx+2. The determinant condition gives P(1)=P(2), so 3a+b=0. Combined with the sum condition, a=−2,b=6. P(4)=−32+24+2=−6.