(D) For the quadratic equation $ax^{2} + bx + c = 0$, the roots are given by the quadratic formula: $x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.Here, $

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(D) For the quadratic equation $ax^{2} + bx + c = 0$, the roots are given by the quadratic formula: $x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.Here, $a = 3$, $b = -2$, and $c = 2$.First, calculate the discriminant $D = b^{2} - 4ac$.$D = (-2)^{2} - 4(3)(2) = 4 - 24 = -20$.Since the discriminant $D The complex roots are $x = \frac{-(-2) \pm \sqrt{-20}}{2(3)} = \frac{2 \pm 2i\sqrt{5}}{6} = \frac{1 \pm i\sqrt{5}}{3}$.

Class 10 Mathematics Quadratic Equations Nature of Roots

Medium

Obtain the roots of the following quadratic equation by using the general formula for the solution: $3x^{2} - 2x + 2 = 0$

A
Roots are $\frac{1 \pm i\sqrt{5}}{3}$
B
Roots are $\frac{1 \pm i\sqrt{5}}{2}$
C
Roots are $\frac{1 \pm \sqrt{5}}{3}$
D
No real roots

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Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $5x^{2} - 3x - 2 = 0$.

Easy

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If the following quadratic equation has two equal and real roots,then find the value of $k$: $2kx^2 - 8x + k = 0$.

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If one root of a quadratic equation $ax^2 + bx + c = 0$ is $\frac{-b + \sqrt{D}}{2a}$,then the other root is $\ldots \ldots \ldots \ldots$.

Easy

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Is the following situation possible? If so,determine their present ages. The sum of the ages of two friends is $20$ years. Four years ago,the product of their ages in years was $48$.

Medium

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Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2} + x - 3 = 0$

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Obtain the roots of the following quadratic equation by using the general formula for the solution: $3x^{2} - 2x + 2 = 0$

Similar Questions

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $5x^{2} - 3x - 2 = 0$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $2kx^2 - 8x + k = 0$.

If one root of a quadratic equation $ax^2 + bx + c = 0$ is $\frac{-b + \sqrt{D}}{2a}$,then the other root is $\ldots \ldots \ldots \ldots$.

Is the following situation possible? If so,determine their present ages. The sum of the ages of two friends is $20$ years. Four years ago,the product of their ages in years was $48$.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $x^{2} + x - 3 = 0$

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