(C) For a quadratic equation $ax^2 + bx + c = 0$ to have two equal and real roots,the discriminant $D$ must be equal to $0$.$D = b^2 - 4ac = 0$Here,$a

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(C) For a quadratic equation $ax^2 + bx + c = 0$ to have two equal and real roots,the discriminant $D$ must be equal to $0$.$D = b^2 - 4ac = 0$Here,$a = 2k$,$b = -8$,and $c = k$.Substituting these values into the discriminant formula:$(-8)^2 - 4(2k)(k) = 0$$64 - 8k^2 = 0$$8k^2 = 64$$k^2 = 8$$k = \pm\sqrt{8}$$k = \pm 2\sqrt{2}$Thus,the values of $k$ are $-2\sqrt{2}$ and $2\sqrt{2}$.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

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

A
$6\sqrt{2}$ and $3\sqrt{2}$
B
$3\sqrt{2}$ and $3\sqrt{2}$
C
$-2\sqrt{2}$ and $2\sqrt{2}$
D
$9\sqrt{3}$ and $2\sqrt{3}$

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Mix Examples - Quadratic Equations

In Hindu civilization,$\ldots \ldots \ldots$ gave the method to solve quadratic equations.

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State whether the following statement is 'True' or 'False'. Justify your answer: If in a quadratic equation the coefficient of $x$ is zero,then the quadratic equation has no real roots.

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Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 11x + 10 = 0$

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Every quadratic polynomial has at the most ......... zero/s.

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Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $2x^{2} - 2\sqrt{6}x + 3 = 0$

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

Similar Questions

In Hindu civilization,$\ldots \ldots \ldots$ gave the method to solve quadratic equations.

State whether the following statement is 'True' or 'False'. Justify your answer: If in a quadratic equation the coefficient of $x$ is zero,then the quadratic equation has no real roots.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 11x + 10 = 0$

Every quadratic polynomial has at the most ......... zero/s.

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $2x^{2} - 2\sqrt{6}x + 3 = 0$

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