(A) For a quadratic equation of the form $ax^{2} + bx + c = 0$,the roots are equal and real if the discriminant $D = b^{2} - 4ac = 0$.Given equation:

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(A) For a quadratic equation of the form $ax^{2} + bx + c = 0$,the roots are equal and real if the discriminant $D = b^{2} - 4ac = 0$.Given equation: $5x^{2} - 2kx + 20 = 0$.Here,$a = 5$,$b = -2k$,and $c = 20$.Substituting these values into the discriminant formula:$(-2k)^{2} - 4(5)(20) = 0$$4k^{2} - 400 = 0$$4k^{2} = 400$$k^{2} = 100$$k = \pm 10$.Thus,the values of $k$ are $10$ and $-10$.

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 $k$: $5x^{2} - 2kx + 20 = 0$.

A
$10$ and $-10$
B
$-10$ and $-10$
C
$10$ and $10$
D
$-10$ and $10$

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If the following quadratic equation has two equal and real roots,then find the value of $k$: $5x^{2} - 2kx + 20 = 0$.

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If one of the roots of $x^{2}-2x-c=0$ is $5$,the other root is ...........

If the radius of a sphere is doubled,its volume becomes $\ldots \ldots \ldots \ldots$ times the original volume.

The sum of a non-zero number and its reciprocal is $\frac{10}{3}$. Find the numbers.

Find the roots of the following quadratic equation by the factorisation method:$3x^{2} + 5\sqrt{5}x - 10 = 0$

The price of corn oil is ₹ $x$ per $kg$. If the price of corn oil is decreased by ₹ $10$ per $kg$,then how many kilograms of corn oil can be obtained for ₹ $500$ at the new rate?

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Find the roots of the following quadratic equation by the factorisation method:
$3x^{2} + 5\sqrt{5}x - 10 = 0$