Match the graphs to the nature of roots of the quadratic equations involved.
((i), (ii) and (iii) stand for real and distinct roots, no real roots and real and equal roots respectively)

A - (i i i), B - (i i)

and

C - (i)

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A - (i), B - (i i)

and

C - (i i i)

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A - (i i), B - (i)

and

C - (i i)

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A - (i), B - (i i i)

and

C - (i i)

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Solution

The correct option is D $A - (i), B - (i i i)$ and $C - (i i)$
When a quadratic equation has real and distinct roots, its graph cuts the $X$ -axis at two points. Thus, equation represented by graph A has real and distinct roots.
When the equation has real and equal roots, its graph touches the $X$ -axis at one point alone. The equation representing graph B has two real and equal roots. Also, observe from the graph that the roots are integers in this case, i.e., 2.
And when the quadratic equation has no real roots, the graph lies completely above X-axis. Thus, the equation representing graph C has no real roots.
Thus, $A - (i), B - (i i i)$ and $C - (i i)$ is the correct option.

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Question 8
The quadratic equation $2 x^{2} - \sqrt{5} x + 1 = 0$ has
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Match the graphs to the nature of roots of the quadratic equations involved. ((i), (ii) and (iii) stand for real and distinct roots, no real roots and real and equal roots respectively)

Match the graphs to the nature of roots of the quadratic equations involved.
((i), (ii) and (iii) stand for real and distinct roots, no real roots and real and equal roots respectively)