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State True or False. The quadratic equation the sum of whose roots is the sum of the roots of $$5x^2 + 4x - 3 = 0$$ and the product of the roots is the product of the roots of $$7x^2 + 24x + 2 = 0$$ has real roots.
Correct Answer: False
The required sum is $$-\frac{4}{5}$$ and the product is $$\frac{2}{7}$$, so the equation is $$x^2 + \frac{4}{5}x + \frac{2}{7} = 0$$. Its discriminant is $$\frac{16}{25} - \frac{8}{7} = \frac{112 - 200}{175} < 0$$, so the roots are not real. The statement is False.
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