(A) The given quadratic equation is $\sqrt{3}x^{2} - 2x + \sqrt{3} = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we get $a = \sqrt{

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(A) The given quadratic equation is $\sqrt{3}x^{2} - 2x + \sqrt{3} = 0$.Comparing this with the standard form $ax^{2} + bx + c = 0$,we get $a = \sqrt{3}$,$b = -2$,and $c = \sqrt{3}$.First,we calculate the discriminant $D = b^{2} - 4ac$.$D = (-2)^{2} - 4(\sqrt{3})(\sqrt{3})$$D = 4 - 4(3) = 4 - 12 = -8$.Since the discriminant $D < 0$,the equation has no real roots in the set of real numbers $R$.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

Easy

Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $\sqrt{3}x^{2} - 2x + \sqrt{3} = 0$

A
No real solution
B
$x = \frac{1 \pm i\sqrt{2}}{\sqrt{3}}$
C
$x = \frac{1 \pm \sqrt{2}}{\sqrt{3}}$
D
$x = \sqrt{3}, -\sqrt{3}$

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Mix Examples - Quadratic Equations

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

Easy

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Find whether the following equation has real roots. If real roots exist,find them.
$\frac{1}{2x-3} + \frac{1}{x-5} = 1, x \neq \frac{3}{2}, 5$

Difficult

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Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 12x + 9 = 0$.

Easy

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If the following quadratic equation has two equal and real roots,then find the value of $k$: $x^{2} - kx + 25 = 0$.

Medium

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If $x=\sqrt{2}$ is one of the roots of the equation $ax^{2}+\sqrt{2}bx+2c=0$; $a \neq 0$,$a, b, c \in R$,then prove that $a+b+c=0$.

Difficult

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Solve the following equation using the quadratic formula,if the equation has a solution in $R$: $\sqrt{3}x^{2} - 2x + \sqrt{3} = 0$

Similar Questions

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

Find whether the following equation has real roots. If real roots exist,find them.$\frac{1}{2x-3} + \frac{1}{x-5} = 1, x \neq \frac{3}{2}, 5$

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $4x^{2} + 12x + 9 = 0$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $x^{2} - kx + 25 = 0$.

If $x=\sqrt{2}$ is one of the roots of the equation $ax^{2}+\sqrt{2}bx+2c=0$; $a \neq 0$,$a, b, c \in R$,then prove that $a+b+c=0$.

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

Find whether the following equation has real roots. If real roots exist,find them.
$\frac{1}{2x-3} + \frac{1}{x-5} = 1, x \neq \frac{3}{2}, 5$