(B) The given quadratic equation is $2x^{2} + 5x - k = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we get $a = 2$,$b = 5$,and $c =

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(B) The given quadratic equation is $2x^{2} + 5x - k = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we get $a = 2$,$b = 5$,and $c = -k$.The discriminant $D$ is given by the formula $D = b^{2} - 4ac$.Given that $D = 81$,we substitute the values:$81 = (5)^{2} - 4(2)(-k)$$81 = 25 + 8k$$81 - 25 = 8k$$56 = 8k$$k = \frac{56}{8} = 7$.Therefore,the value of $k$ is $7$.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

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If $81$ is the discriminant of $2x^{2} + 5x - k = 0$,then the value of $k$ is ..............

A
$5$
B
$7$
C
$-7$
D
$2$

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Mix Examples - Quadratic Equations

If the value of the discriminant of a quadratic equation $kx^2 - 6x + 1 = 0$ is $0$,then $k = \ldots$

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Solve the following equation using the method of factorization and write its solution set: $\frac{x+1}{x+2} + \frac{1}{x} = \frac{5}{4}$

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If the following quadratic equation has two equal and real roots,then find the value of $k$: $x^{2} + 2kx + 4 = 0$.

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The symbol used for the discriminant of a quadratic equation is $\ldots \ldots \ldots \ldots .$

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Obtain the roots of the following equation using the method of 'completing the square': $3y^{2} + 7y - 20 = 0$.

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If $81$ is the discriminant of $2x^{2} + 5x - k = 0$,then the value of $k$ is ..............

Similar Questions

If the value of the discriminant of a quadratic equation $kx^2 - 6x + 1 = 0$ is $0$,then $k = \ldots$

Solve the following equation using the method of factorization and write its solution set: $\frac{x+1}{x+2} + \frac{1}{x} = \frac{5}{4}$

If the following quadratic equation has two equal and real roots,then find the value of $k$: $x^{2} + 2kx + 4 = 0$.

The symbol used for the discriminant of a quadratic equation is $\ldots \ldots \ldots \ldots .$

Obtain the roots of the following equation using the method of 'completing the square': $3y^{2} + 7y - 20 = 0$.

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