<p>Quadratic polynomials <img alt="$P(x)$" height="18" src="https://latex.artofproblemsolving.com/6/e/f/6efaaf74e576202fad965134bc49c6a34aac4c30.png" width="37" /> and <img alt="$Q(x)$" height="18" src="https://latex.artofproblemsolving.com/d/9/d/d9dfe7c7a0b887097fa2227a230fc915ba2e5477.png" width="37" /> have leading coefficients <img alt="$2$" height="12" src="https://latex.artofproblemsolving.com/4/1/c/41c544263a265ff15498ee45f7392c5f86c6d151.png" width="8" /> and <img alt="$-2,$" height="15" src="https://latex.artofproblemsolving.com/8/a/f/8afe6a98f0632a1d5ffbadbcb97205578e7a3dd5.png" width="27" /> respectively. The graphs of both polynomials pass through the two points <img alt="$(16,54)$" height="20" src="https://latex.artofproblemsolving.com/f/b/5/fb51011e48a783a40e23d6e1a0a4b2f9a9b8ec73.png" width="60" /> and <img alt="$(20,53).$" height="20" src="https://latex.artofproblemsolving.com/d/9/1/d9194f5a744476ee9eb8b7349a4aa37ad56d982d.png" width="65" /> Find <img alt="$P(0) + Q(0).$" height="20" src="https://latex.artofproblemsolving.com/a/d/b/adbb2cfc6d430736112efd0c138450fe574a0d52.png" width="104" /></p>

Question No: 429

Quadratic polynomials $P(x)$ and $Q(x)$ have leading coefficients $2$ and $-2,$ respectively. The graphs of both polynomials pass through the two points $(16,54)$ and $(20,53).$ Find $P(0) + Q(0).$

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Tags: Algebra

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