(D) 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 the equati

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(D) 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 the equation $4x^{2} - 5x + k = 0$,we have $a = 4$,$b = -5$,and $c = k$.Substituting these values into the discriminant formula:$D = (-5)^{2} - 4(4)(k) = 0$$25 - 16k = 0$$16k = 25$$k = \frac{25}{16}$

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 $k$: $4x^{2} - 5x + k = 0$.

A
$\frac{25}{49}$
B
$\frac{5}{15}$
C
$\frac{13}{10}$
D
$\frac{25}{16}$

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Mix Examples - Quadratic Equations

Obtain the roots of the following quadratic equation by using the general formula for the solution: $25x^2 + 20x + 7 = 0$.

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The sum of squares of two consecutive odd numbers is $514$. Find those numbers.

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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 $4p - 2q + r = 0$.

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If $\frac{1}{2}$ is a root of the equation $x^{2}+kx-\frac{5}{4}=0$,then the value of $k$ is

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What is the value of $k$ if one of the roots of the quadratic equation $x^{2} + 6x + k = 0$ is $-4$?

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If the following quadratic equation has two equal and real roots,then find the value of $k$: $4x^{2} - 5x + k = 0$.

Similar Questions

Obtain the roots of the following quadratic equation by using the general formula for the solution: $25x^2 + 20x + 7 = 0$.

The sum of squares of two consecutive odd numbers is $514$. Find those numbers.

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 $4p - 2q + r = 0$.

If $\frac{1}{2}$ is a root of the equation $x^{2}+kx-\frac{5}{4}=0$,then the value of $k$ is

What is the value of $k$ if one of the roots of the quadratic equation $x^{2} + 6x + k = 0$ is $-4$?

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