Question

Draw the graph of quadratic polynomial y = x square-5x + 6 and also find its zeros

Answer 1

EXPLANATION.

Graph of the quadratic polynomial,

⇒ y = x² - 5x + 6.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ y = x² - 3x - 2x + 6.

⇒ y = x(x - 3) - 2(x - 3).

⇒ y = (x - 2)(x - 3).

Zeroes of the equation, we get.

⇒ (x - 2)(x - 3) = 0.

⇒ x = 2  and  x = 3.

Put the value of x in equation, we get.

⇒ y = (2)² - 5(2) + 6.

⇒ y = 4 - 10 + 6.

⇒ y = 10 - 10.

⇒ y = 0.

Their Co-ordinates = (2,0).

Put x = 3 in equation, we get.

⇒ y = (3)² - 5(3) + 6.

⇒ y = 9 - 15 + 6.

⇒ y = 15 - 15.

⇒ y = 0.

Their Co-ordinates = (3,0).

Put x = 0 in equation, we get.

⇒ y = (0)² - 5(0) + 6.

⇒ y = + 6.

Their Co-ordinates = (0,6).

Equation y = x² - 5x + 6 makes upwards parabola.

Answer 2

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Solution

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The given quadratic equation is x²-5x+ 6=0.

Lety =x²-5x + 6, when we substitute

➦ different values ofx in the equation y = x²-5x +6 then value of y changes accordingly.

☯ When x=0 then ;

➦ y (0)²- (5 x 0) +6 = 0-0+6 = 6

▫ The point is (0,6) ✔

☯ When x =2 then ;

➦ y= (2) ² - (5 x 2) +6 = 4 - 10 + 6 =10- 10 =0

▫ The point is (2,0) ✔

☯ When x = 3 then ;

➦ y (3)² - (5 x 3) +6 = 9- 15+6 = 15- 15 = 0

▫ The point is (3,0) ✔

➦ Therefore, the coordinates are (0,6),

➦ (2,0) and ( 3, 0) and the graph of the quadratic equationy = x² -5x +6 is as ;

⚛ shown above ⚛

➦ Hence, from above graph, we get that graph is forming parabola

==>x = 2 or x = 3✔