Question

.
Find the zeroes of the quadratic polynomial
x²+2tio and verify the relationship
between the zeroes and the co-efficiet
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Answer 1

Answer:

Given polynomial is

x^{2} + 3x + 2x

2

+3x+2 -----------------------(1)

If x_{1}, x_{2}x

1

,x

2

are roots of a polynomial, then the polynomial is written as

x^{2} - (x_{1} + x_{2} )x + x_{1} x_{2}x

2

−(x

1

+x

2

)x+x

1

x

2

-----------------------(2)

Writing (1) in the form of (2), we get

x^{2} - (-2 - 1)x + 2x

2

−(−2−1)x+2

Comparing a and b, we get

x_{1} = -2, x_{2} = -1x

1

=−2,x

2

=−1

Hence, the roots of given polynomial are 2, 1.

Verification of relationships:

(i) Sum of roots = \frac{- coefficient of x}{coefficient of x^{2}}

coefficientofx

2

−coefficientofx

=

-2-1 = -3/1

-3 = -3

(ii) Product of roots = \frac{constant}{- coefficient of x^{2}}

−coefficientofx

2

constant

(-2)(-1) = 2/1

2 = 2

Step-by-step explanation:

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Answer 2

Answer:

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