Question

The curve which represents a quadratic polynomial meets the X-axis at (2, 0) and ( - 2,0). Form the quadratic polynomial.

Answer 1

Answer:

Step-by-step explanation:

The curve meets x axis at (2,0) and (-2,0)

hence x=2 and x=-2

so the zeros of polynomial are 2 and -2

The polynomial with α and β is given by

x²-( α + β)x+ αβ

=x²-(2-2)x+2(-2)

=x²-4

Answer 2

Answer:

The equation of curve representing a quadratic polynomial meeting the x-axis at ( 2 , 0) and ( -2 , 0 ) is x² - 4 = 0.

Step-by-step explanation:

Given :

• Curve of polynomial meet the x-axis at (2 , 0) and (-2 , 0)

Solution :

• The curve of the polynomial meet the x-axis at ( 2, 0 ) and (-2 , 0 ).
• The point A ( 2 , 0 ) and B ( -2 , 0 ) satisfy the equation of the curve. Hence, are zeros of the quadratic polynomial.
• The equation of the polynomial whose zeros α and β are given by

${x}^{2} - (sum \: of \: zeos) + (product \: of \: zeros) = 0 \\ {x}^{2} - ( \alpha + \beta ) + ( \alpha \beta) = 0$

• Sum of zeros, α + β = ( -2 + 2 ) = 0
• Product of zeros, αβ = ( 2 x -2 ) = -4
• Equation of the polynomial is

${x}^{2} - (0)x + ( - 4) = 0 \\ {x}^{2} - 4 = 0$

• Hence, equation of the polynomial is x² - 4 .