(C) To determine which quadratic equation has a root $x=3$,we substitute $x=3$ into each equation:For option $C$: $x^{2}-8x+15=0$Substituting $x=3$: $

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(C) To determine which quadratic equation has a root $x=3$,we substitute $x=3$ into each equation:For option $C$: $x^{2}-8x+15=0$Substituting $x=3$: $(3)^{2}-8(3)+15 = 9-24+15 = 24-24 = 0$.Since the result is $0$,$x=3$ is a root of the equation $x^{2}-8x+15=0$.

Class 10 Mathematics Quadratic Equations Mix Examples - Quadratic Equations

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The quadratic equation .............. has a root $x=3$.

A
$x^{2}-8x-15=0$
B
$x^{2}+8x+15=0$
C
$x^{2}-8x+15=0$
D
$x^{2}+8x-15=0$

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Mix Examples - Quadratic Equations

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The quadratic equation .............. has a root $x=3$.

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If $x=-2$ is a solution of a quadratic equation $k x^{2}+5 x+2=0,$ then $k=\ldots \ldots \ldots \ldots$

Obtain the roots of the following quadratic equation by using the quadratic formula: $2x^{2} + 5\sqrt{3}x + 6 = 0$.

If one root of $x^{2}-5x+6=0$ is also the root of $x^{2}+3x+c=0$,then $c = \ldots$

Find whether the following equation has real roots. If real roots exist,find them.$8 x^{2}+2 x-3=0$

The roots of $4x^{2} + 2x + \frac{1}{4} = 0$ are $\ldots \ldots \ldots \ldots.$

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Find whether the following equation has real roots. If real roots exist,find them.
$8 x^{2}+2 x-3=0$