(C) For a quadratic equation $ax^2 + bx + c = 0$,the discriminant is given by $D = b^2 - 4ac$.$1$. If $D > 0$,the equation has two distinct real roots

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(C) For a quadratic equation $ax^2 + bx + c = 0$,the discriminant is given by $D = b^2 - 4ac$.$1$. If $D > 0$,the equation has two distinct real roots.$2$. If $D = 0$,the equation has two equal real roots.$3$. If $D Thus,the condition for the non-existence of real roots is $D < 0$.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

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If $\ldots \ldots \ldots$ then real roots of a quadratic equation do not exist.

A
$D=0$
B
$D > 0$
C
$D < 0$
D
$D=1$

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Mix Examples - Quadratic Equations

Obtain the roots of the following quadratic equation by using the quadratic formula: $p^{2} x^{2} + (p^{2} - q^{2}) x - q^{2} = 0$

Medium

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State whether the quadratic equation $\sqrt{2} x^{2}-\frac{3}{\sqrt{2}} x + \frac{1}{\sqrt{2}} = 0$ has two distinct real roots. Justify your answer.

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Verify whether the given value of $x$ is a solution of the quadratic equation or not: $(x-2)(x+3)+1=0$; $x=2$.

Medium

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In quadratic equation $ax^{2} + bx + c = 0$,where $a \neq 0$,$b = 0$,and $D > 0$,then both the roots of the equation are .....

Easy

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If $-3$ is a root of a quadratic equation $x^{2}+3(k+2)x-9=0$,then $k=\ldots \ldots \ldots \ldots .$

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If $\ldots \ldots \ldots$ then real roots of a quadratic equation do not exist.

Similar Questions

Obtain the roots of the following quadratic equation by using the quadratic formula: $p^{2} x^{2} + (p^{2} - q^{2}) x - q^{2} = 0$

State whether the quadratic equation $\sqrt{2} x^{2}-\frac{3}{\sqrt{2}} x + \frac{1}{\sqrt{2}} = 0$ has two distinct real roots. Justify your answer.

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $(x-2)(x+3)+1=0$; $x=2$.

In quadratic equation $ax^{2} + bx + c = 0$,where $a \neq 0$,$b = 0$,and $D > 0$,then both the roots of the equation are .....

If $-3$ is a root of a quadratic equation $x^{2}+3(k+2)x-9=0$,then $k=\ldots \ldots \ldots \ldots .$

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