How many real solutions are there for $5 x^{2} + 7 x + 2$ $5x^2+7x+2$ ?

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How many real solutions are there for $5 x^{2} + 7 x + 2$ $5x^2+7x+2$ ?

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Answer 1 · 2017-01-09T22:38:54

Two real solutions

Explanation:

Without solving the equation, you can decide whether the solutions are real or not, by calculating the expression under square root in the quadratic formula - if it is null or positive, there are real solutions, otherwise the solutions are complex.

Then $b^{2} - 4 a c = 7^{2} - 4 \cdot 5 \cdot 2 = 49 - 40 = 9 > 0$ $b^2-4ac=7^2-4*5*2=49-40=9>0$

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How many real solutions are there for $5 x^{2} + 7 x + 2$ $5x^2+7x+2$ ?

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