(C) To determine how the graph of $p(x) = x^{2} + 6x + 9$ intersects the $X$-axis,we find the zeros of the polynomial by setting $p(x) = 0$.$x^{2} + 6

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(C) To determine how the graph of $p(x) = x^{2} + 6x + 9$ intersects the $X$-axis,we find the zeros of the polynomial by setting $p(x) = 0$.$x^{2} + 6x + 9 = 0$This is a perfect square trinomial,which can be factored as $(x + 3)^{2} = 0$.Thus,$x = -3$ is the only root (a repeated root).Since there is only one distinct real root,the parabola represented by the quadratic polynomial touches the $X$-axis at exactly one point,which is $(-3, 0)$.

Class 10 Mathematics Polynomials Mix Examples - Polynomials

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The graph of $p(x) = x^{2} + 6x + 9$ intersects the $X$-axis $\ldots \ldots \ldots \ldots$

A
in two distinct points
B
in three distinct points
C
touches
D
does not intersect

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Mix Examples - Polynomials

Which of the following groups matches the data of Part $I$ with the data of Part $II$?

Part $I$ Part $II$

$1.$ The graph of $p(x)=x^{2}-5x+6$ $a.$ Intersects the $X$-axis at one point.

$2.$ The graph of $p(x)=x^{2}-10x+25$ $b.$ Intersects the $X$-axis at zero points.

$3.$ The graph of $p(x)=x^{3}-4x$ $c.$ Intersects the $X$-axis at two points.

$4.$ The graph of $p(x)=x^{2}+4x+5$ $d.$ Intersects the $X$-axis at three points.

Difficult

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Find the number of real zeros of the following polynomial: $p(x) = 5x - 4$.

Easy

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The product of the zeros of $p(x) = 4x^{2} + 12x + 5$ is..........

Easy

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Find the division of the following by synthetic division method: $p(x) = x^{4} + 1$ by $x + 1$.

Medium

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Answer the following and justify: What will be the quotient and remainder on division of $ax^{2} + bx + c$ by $px^{3} + qx^{2} + nx + s$,where $p \neq 0$?

Medium

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Part $I$	Part $II$
$1.$ The graph of $p(x)=x^{2}-5x+6$	$a.$ Intersects the $X$-axis at one point.
$2.$ The graph of $p(x)=x^{2}-10x+25$	$b.$ Intersects the $X$-axis at zero points.
$3.$ The graph of $p(x)=x^{3}-4x$	$c.$ Intersects the $X$-axis at two points.
$4.$ The graph of $p(x)=x^{2}+4x+5$	$d.$ Intersects the $X$-axis at three points.

The graph of $p(x) = x^{2} + 6x + 9$ intersects the $X$-axis $\ldots \ldots \ldots \ldots$

Similar Questions

Find the number of real zeros of the following polynomial: $p(x) = 5x - 4$.

The product of the zeros of $p(x) = 4x^{2} + 12x + 5$ is..........

Find the division of the following by synthetic division method: $p(x) = x^{4} + 1$ by $x + 1$.

Answer the following and justify: What will be the quotient and remainder on division of $ax^{2} + bx + c$ by $px^{3} + qx^{2} + nx + s$,where $p \neq 0$?

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