What can be said about the roots of the equation 4x^2 + 9x – 7 = 0 without actually solving it?

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We have to find the properties of the roots of the given equation without solving it. We can determine if the roots are real or complex and whether they are the same or different.

For the equation 4x^2 + 9x – 7 = 0 we see that the discriminant b^2 – 4ac = 9^2 + 4*7*4

=> 81 + 56

=> 137

This is neither 0 nor negative. The discriminant is positive.

**This gives us that 4x^2 + 9x – 7 has two distinct real roots. **

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