Question

draw the graph of the polynomial x^2+2x-15​

Answer 1

EXPLANATION.

Graph of the polynomial,

⇒ y = x² + 2x - 15.

Factorizes the equation into middle term splits, we get.

⇒ y = x² + 5x - 3x - 15.

⇒ y = x(x + 5) -3(x + 5).

⇒ y = (x - 3)(x + 5).

⇒ (x - 3)(x + 5) = 0.

⇒ x = 3  and  x = -5.

Put the value of x = 3 in equation, we get.

⇒ y = (3)² + 2(3) - 15.

⇒ y = 9 + 6 - 15.

⇒ y = 15 - 15.

⇒ y = 0.

Their Co-ordinates = (3,0).

Put the value of x = -5 in equation, we get.

⇒ y = (-5)² + 2(-5) - 15.

⇒ y = 25 - 10 - 15.

⇒ y = 25 - 25.

⇒ y = 0.

Their Co-ordinates = (-5,0).

Put x = 0 in equation, we get.

⇒ y = (0)² + 2(0) - 15.

⇒ y = 0 + 0 - 15.

⇒ y = -15.

Their Co-ordinates = (0,-15)

Answer 2

$\large\underline{\red{\sf \green{\bigstar} Correct\;Question}}$

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• draw the graph of the polynomial x^2+2x-15

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠ y = x² + 2x - 15.

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$\large\underline{\blue{\sf \orange{\bigstar} Solution:-}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\pink{\sf{\star\;Factorizes\; the \;equation \;into\; middle \;term \;splits, \;we \;get}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠ y = x² + 5x - 3x - 15.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠ y = x(x + 5) -3(x + 5).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠ y = (x - 3)(x + 5).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠ (x - 3)(x + 5) = 0.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠x = 3  and  x = -5.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\red{\sf{\star\;Put \;the\; value \;of \;x\; =\; 3\; in\; equation,\; we \;get.}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠ y = (3)² + 2(3) - 15.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠ y = 9 + 6 - 15.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠ y = 15 - 15.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠ y = 0.

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☯ Co-ordinates = (3,0).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\blue{\sf{\star\;Put\; the \;value \;of \;x\; =\; -5\; in\; equation, \;we\; get}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠y = (-5)² + 2(-5) - 15.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠y = 25 - 10 - 15.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠y = 25 - 25.

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• ➠ y = 0.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

☯ Co-ordinates = (-5,0).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\orange{\sf{\star\;Put \;x \;= \;0 \;in\; equation,\; we\; get.}}$

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• ➠ y = (0)² + 2(0) - 15.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ➠y = 0 + 0 - 15.

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• ➠y = -15.

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$\purple{\sf{\star\;➥ \;Their\; Co\;-\;ordinates\; = (0,-15)}}$

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