Math, asked by ajaipandey1893, 7 hours ago

draw the graph of polynomial y = -2x^2+5x+3

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Answered by xSoyaibImtiazAhmedx

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Answered by amansharma264

Graph of the polynomial.

⇒ -2x² + 5x + 3 = 0.

As we know that,

Take (-) sign in common, we get.

⇒ -(2x² - 5x - 3) = 0.

⇒ 2x² - 5x - 3 = 0.

Factorizes the equation into middle term splits, we get.

⇒ 2x² - 6x + x - 3 = 0.

⇒ 2x(x - 3) + 1(x - 3) = 0.

⇒ (2x + 1)(x - 3) = 0.

⇒ x = -1/2 and x = 3.

⇒ y = 2x² - 5x - 3.

Put the value of x = -1/2 in the equation, we get.

⇒ y = 2(-1/2)² - 5(-1/2) - 3.

⇒ y = 2/4 + 5/2 - 3.

⇒ y = 1/2 + 5/2 - 3.

⇒ y = 1 + 5 - 6/2.

⇒ y = 6 - 6/2.

⇒ y = 0.

Their Co-ordinates = (-1/2.0).

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

⇒ y = 2x² - 5x - 3.

⇒ y = 2(3)² - 5(3) - 3.

⇒ y = 18 - 15 - 3.

⇒ y = 18 - 18.

⇒ y = 0.

Their Co-ordinates = (3,0).

Put the value of x = 0 in the equation, we get.

⇒ y = 2x² - 5x - 3.

⇒ y = 2(0)² - 5(0) - 3.

⇒ y = - 3.

Their Co-ordinates = (0,-3).

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