(B) The given quadratic equation is $x^{2}-10x+(2k-1)=0$.Comparing this with the standard form $ax^{2}+bx+c=0$,we get $a=1$,$b=-10$,and $c=2k-1$.The d

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(B) The given quadratic equation is $x^{2}-10x+(2k-1)=0$.Comparing this with the standard form $ax^{2}+bx+c=0$,we get $a=1$,$b=-10$,and $c=2k-1$.The discriminant $D$ is given by the formula $D=b^{2}-4ac$.Given $D=40$,we substitute the values:$40 = (-10)^{2} - 4(1)(2k-1)$$40 = 100 - 4(2k-1)$$40 = 100 - 8k + 4$$40 = 104 - 8k$$8k = 104 - 40$$8k = 64$$k = 8$.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

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If the discriminant of $x^{2}-10x+(2k-1)=0$ is $40$,then $k=$...............

A
$79$
B
$8$
C
$13$
D
$15$

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Mix Examples - Quadratic Equations

If one of the roots of the equation $px^{2} + qx + r = 0$ where $p \neq 0$ and $p, q, r \in R$ is $x = -2$,then prove that $4p - 2q + r = 0$.

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Find the roots of the following quadratic equations by the factorisation method:
$\frac{2}{5} x^{2}-x-\frac{3}{5}=0$

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The sum of two numbers is $15$. If the sum of their reciprocals is $\frac{3}{10}$,then find the numbers.

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Which constant should be added and subtracted to solve the quadratic equation $4x^{2} - \sqrt{3}x - 5 = 0$ by the method of completing the square?

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If the value of the discriminant of the quadratic equation $x^{2}-10x+(2k-1)=0$ is $40$,then $k = \ldots$.

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If the discriminant of $x^{2}-10x+(2k-1)=0$ is $40$,then $k=$...............

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If one of the roots of the equation $px^{2} + qx + r = 0$ where $p \neq 0$ and $p, q, r \in R$ is $x = -2$,then prove that $4p - 2q + r = 0$.

Find the roots of the following quadratic equations by the factorisation method:$\frac{2}{5} x^{2}-x-\frac{3}{5}=0$

The sum of two numbers is $15$. If the sum of their reciprocals is $\frac{3}{10}$,then find the numbers.

Which constant should be added and subtracted to solve the quadratic equation $4x^{2} - \sqrt{3}x - 5 = 0$ by the method of completing the square?

If the value of the discriminant of the quadratic equation $x^{2}-10x+(2k-1)=0$ is $40$,then $k = \ldots$.

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Find the roots of the following quadratic equations by the factorisation method:
$\frac{2}{5} x^{2}-x-\frac{3}{5}=0$