The nature of the roots of the quadratic equation 4x²-12x + 9=0 is two real and identical roots.
The nature of the roots of a quadratic equation can be determined by analyzing the discriminant, which is the expression inside the square root of the quadratic formula. In the quadratic equation ax² + bx + c = 0, the discriminant is given by b² - 4ac. If the discriminant is greater than zero, the equation has two real and distinct roots. If the discriminant is equal to zero, the equation has two real and identical roots. And if the discriminant is less than zero, the equation has no real roots, only complex roots.
Using the given quadratic equation 4x² - 12x + 9 = 0, we can find the discriminant as follows: D = (-12)² - 4(4)(9) = 144 - 144 = 0. Since the discriminant is equal to zero, the equation has two real and identical roots.
Therefore, the nature of the roots of the quadratic equation 4x² - 12x + 9 = 0 is two real and identical roots.
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