book Maths Puzzle Numerical Ability

Without solving the quadratic equation 5x^2 + 8x + 6 = 0, state whether or not this quadratic equation has real roots. Justify your answer.

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I need a theorem for congruence of matrix(a big one) What would be another way to add 1+3+5+7+9+....499=to equal the sum of 62,500?
Only using odd numbers. We need another way to find the sum of all the odd numbers from 1 to 499 and equal 62,500