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Find the discriminant of the quadratic equation 2x2 − 4x + 3 = 0 and hence find the nature of its roots. |
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Answer» Given quadratic equation is 2x2 − 4x + 3 = 0. By comparing given quadratic equation with standard quadratic equation ax2 + bx + c = 0, we get a = 2, b = −4 and c = 3. Now, the discriminant of given quadratic equation is D = b2 − 4ac = (−4)2 − 4 × 2 × 3 = 16 − 24 = −8 < 0. Hence, both roots are imaginary i.e., both roots are not real. (Because, if D = b2 − 4ac < 0, then its roots are imaginary means no real roots.) Hence, the quadratic equation 2x2 − 4x + 3 = 0 has no real roots. |
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