It is known that x=7 is a root of the equation ax^2 + bx + 2 = 0, where a<0. Solve the inequality ax²4 + bx^2 + 2>0.

Question

Cornelius Daniels

Mathematics

Yesterday, 22:18

It is known that x=7 is a root of the equation ax^2 + bx + 2 = 0, where a<0. Solve the inequality ax²4 + bx^2 + 2>0.

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Answers (1)

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Myla Conrad · Answer 1

2 / (7a) < x < 7

Step-by-step explanation:

The product of roots of ax² + bx + c is c/a. In this case, that means the second root of the equation is ...

... 2 / (7a)

Since a < 0, the parabola opens downward and 2 / (7a) < 0. The quadratic function will be positive between the two roots, on the interval ...

... 2 / (7a) < x < 7