Name: Rational Expressions: Operations and Manipulations
Uploaded: 2019-07-19
Duration: 12 min 15 s
Description: In this video, we will learn the concept of multiplying, simplifying and cancelling the common factors with detailed examples. View the video now.

Question

Connect the graphs to their respective number of points of intersection with $X$ -axis and to their corresponding nature of solutions which is given in the following table.

S.No.	Graphs	Number of points of intersection with $X$ -axis	Nature of solutions
$1 .$		$2$	Real and equal roots
$2 .$		$1$	No real roots
$3 .$		$2$	No real roots
$4 .$		$0$	Real and equal roots
$5 .$		$0$	Real and unequal roots
$6 .$		$1$	Real and unequal roots

Accepted Answer

We have connected the graphs to its respective number of points of intersection with $x$ -axis and to its corresponding nature of solutions shown in the following table.

S.No. Graphs Number of points of intersection with $X$ -axis Nature of solutions

$1 .$ $0$ No real roots

$2 .$ $2$ Real and unequal roots

$3 .$ $0$ No real roots

$4 .$ $1$ Real and equal roots

$5 .$ $2$ Real and unequal roots

$6 .$ $1$ Real and equal roots

Graphs- $1 & 3$ are not touching with the $x$ -axis. Thus, they have $0$ roots meaning roots are not real.

Graphs- $2 & 5$ are intersecting at $2$ different points. Thus, they have $2$ roots and roots are real and unequal.

Graphs- $4 & 6$ are touching the $x$ -axis at $1$ point each. Thus, they have $1$ root each or we can say each of them have two roots which are equal. Roots are real and equal.

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