(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 Mix Examples - Quadratic Equations

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 method of factorization and write its solution set: $\frac{1}{x-2}+\frac{1}{x+3}=\frac{7}{2x}$ $(x \neq 2, x \neq -3, x \neq 0)$

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$(x+6)(x+5)=0$ is a ....... .

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The name of the Indian mathematician who gave the formula for finding the roots of the quadratic equation $ax^2 + bx + c = 0$ by the method of completing the square is ..... .

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

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Solve the following equation using the method of factorization and write its solution set: $\frac{1}{x-2}+\frac{1}{x+3}=\frac{7}{2x}$ $(x \neq 2, x \neq -3, x \neq 0)$

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $x^{2}+\sqrt{2}x-4=0$; $x=-2\sqrt{2}$.

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $2x^{2} - 6x + 3 = 0$; $x = \frac{1}{2}$.

$(x+6)(x+5)=0$ is a ....... .

The name of the Indian mathematician who gave the formula for finding the roots of the quadratic equation $ax^2 + bx + c = 0$ by the method of completing the square is ..... .

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