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3) when determinants of a quadratic polynomial is equal to zero, the polynomial has only one root
determinant D of a quadratic equation of the form ax^2 + bx + c = 0 is given by
D = b^2 - 4ac
if D = 0, the roots are equal i.e. only one root is there.
4) when D < 0, there is no root in real numbers
x^2 + x + 1 = 0
3x^2 + 4x + 2 = 0
x^2 + 5x + 7 = 0
in all the above cases, D < 0, so the equation will not have any real roots
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