(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: $k x^{2} - 2 \sqrt{5} x + 4 = 0$.Here,$a = k$,$b = -2 \sqrt{5}$,and $c = 4$.Substituting these values into the discriminant formula:$(-2 \sqrt{5})^{2} - 4(k)(4) = 0$$(4 \times 5) - 16k = 0$$20 - 16k = 0$$16k = 20$$k = \frac{20}{16} = \frac{5}{4}$.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

Medium

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

A
$\frac{5}{4}$
B
$\frac{15}{3}$
C
$\frac{4}{1}$
D
$\frac{10}{3}$

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

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Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $\frac{1}{4} x^{2} - 2x + 1 = 0$.

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $\sqrt{2} x^{2}+7 x+5 \sqrt{2}=0, x=-\sqrt{2}$

The golden ratio,often denoted by the Greek letter $\phi$,is a special number. Which of the following is the golden number?

If one of the roots of $2x^{2} + 5x + 3 = 0$ is $-1$,the other root is .............

Find the discriminant of the following quadratic equation: $5x^{2} - 4\sqrt{2}x - 1 = 0$.

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