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Write the nature of the roots quadratic equation 2x²-5x 6=0?

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So, Nature of the roots £,β of any quadratic equation, depends on the expression (b² -4ac) , ie, this expression discriminates the roots of the quadratic equation. So, we call it Discriminant ( D) = b² - 4ac. So, 'D' of 2x² - 5x + 6 =0. = 25 - 48 = - 23. Since it is negative, or D < 0. So, the equation has IMAGINARY & UNEQUAL roots. read more

Nature of Roots (1) Equation ax2 + bx + c = 0; a ¹0 will have real roots only when D = b2 - 4ac > 0. (2) When D = b2 - 4ac<0, then the equation ax2 + bx + c = 0 will have no real roots. (3) When D = b2 - 4ac = 0, then the roots will be real and equal, each being equal to . read more

When a, b and c are real numbers, a ≠ 0 and discriminant is negative , then the roots α and β of the quadratic equation ax 2 + bx + c = 0 are unequal and imaginary. Here the roots α and β are a pair of the complex conjugates. read more

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