Solve the quadratic equation $x^2 + 4x + 4 = 0$ and explain the nature of its roots.

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Accepted Answer

Solution of the Quadratic Equation Step 1: Compare the given equation with the standard form of a quadratic equation
The given equation is $x^2 + 4x + 4 = 0$, which can be compared with the standard form of a quadratic equation $ax^2 + bx + c = 0$. Step 2: Calculate the discriminant
The discriminant of the quadratic equation is given by $D = b^2 - 4ac$. In this case, $a = 1$, $b = 4$, and $c = 4$. Therefore, $D = (4)^2 - 4(1)(4) = 16 - 16 = 0$. Step 3: Determine the nature of the roots
Since the discriminant is zero, the quadratic equation has equal roots. The roots can be calculated using the formula $x = \frac{-b}{2a}$. In this case, $x = \frac{-4}{2(1)} = -2$. Conclusion
The quadratic equation $x^2 + 4x + 4 = 0$ has equal roots, both of which are $-2$.

CBSE · Class 10 · Mathematics · Quadratic EquationsSolve the quadratic equation $x^2 + 4x + 4 = 0$ and explain the nature of its roots.

Solution of the Quadratic Equation

Step 1: Compare the given equation with the standard form of a quadratic equation\nThe given equation is $x^2 + 4x + 4 = 0$, which can be compared with the standard form of a quadratic equation $ax^2 + bx + c = 0$.

Step 2: Calculate the discriminant\nThe discriminant of the quadratic equation is given by $D = b^2 - 4ac$. In this case, $a = 1$, $b = 4$, and $c = 4$. Therefore, $D = (4)^2 - 4(1)(4) = 16 - 16 = 0$.

Step 3: Determine the nature of the roots\nSince the discriminant is zero, the quadratic equation has equal roots. The roots can be calculated using the formula $x = \frac{-b}{2a}$. In this case, $x = \frac{-4}{2(1)} = -2$.

Conclusion\nThe quadratic equation $x^2 + 4x + 4 = 0$ has equal roots, both of which are $-2$.