Given two quadratic equations: Equation I: p x 2 − 9 x + 7 = 0 p x^2 - 9x + 7 = 0 p x 2 − 9 x + 7 = 0 Equation II: q y 2 − 8 y + 4 = 0 q y^2 - 8y + 4 ...

Question

Given two quadratic equations:

Equation I: px29x+7=0p x^2 - 9x + 7 = 0

Equation II: qy28y+4=0q y^2 - 8y + 4 = 0

where pp and qq are positive integers, and one root of Equation II is 23\frac{2}{3}. The ratio of the highest root of Equation I to the highest root of Equation II is 7:47 : 4.

Find the value of (p+q)(p + q).

Options

A.

5

B.

3

C.

7

D.

8

quadratic equationsrootsratioalgebra

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