Question

construct a quadratic polynomial whose zeroes are 1 and -3 . verify the relation between the coefficients and zeroes of polynomial .

Answer 1

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Given,

Zeroes of a quadratic polynomial is 1 and -3.

Sum of zeroes = 1 - 3 = -2.

Product of zeroes = 1 ( -3 ) = -3.

The general form of a quadratic equation is :

= x² - ( Sum of zeroes ) x + Product of zeroes

= x² - ( -2 ) x + ( -3 )

= x² + 2x - 3.

Now,

⇒ Sum of zeroes = - coefficient of x / coefficient of x²

⇒ 1 - 3 = - 2 / 1

∴  -2 = -2.

⇒ Product of zeroes = Constant term / coefficient of x²

⇒ 1 ( -3 ) = -3 / 1

∴ -3 = -3

Verified.

The required polynomial is x² + 2x - 3.


Hope it helps !

Answer 2

Let alfa be 1 and beta be -3
Sum of zeros = 1-3
=-2
Product of zeros=1×(-3)
=-3
The required polynomial is,
x2-(a+b)x+ab
x2-(-2)x+(-3)
x2+2x-3
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