(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

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

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The roots of the quadratic equation $x + \frac{2}{x} = 3$ are $\dots$ $(x \neq 0)$.

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

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Find whether the following equation has real roots. If real roots exist,find them.
$5x^{2}-2x-10=0$

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Verify whether the given value of $x$ is a solution of the quadratic equation or not: $2x^{2} - 6x + 3 = 0$; $x = \frac{1}{2}$.

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

Similar Questions

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

The roots of the quadratic equation $x + \frac{2}{x} = 3$ are $\dots$ $(x \neq 0)$.

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

Find whether the following equation has real roots. If real roots exist,find them.$5x^{2}-2x-10=0$

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $2x^{2} - 6x + 3 = 0$; $x = \frac{1}{2}$.

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Find whether the following equation has real roots. If real roots exist,find them.
$5x^{2}-2x-10=0$