Question

If a & ß are the zeroes of a quadratic polynomial
P(y) = 4y2 – 12y + 9 then find the zeroes and verify the relation
between zeroes and coefficients.​

Answer 1

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10th

Maths

Polynomials

Relationship between Zeroes and Coefficients of a Polynomial

Find the zeros of the follo...

MATHS

Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.

4u

2

+8u

HARD

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ANSWER

Let f(u)=4u

2

+8u

To calculate the zeros of the given equation, put f(u)=0.

4u

2

+8u=0

4u(u+2)=0

u=0,u=−2

The zeros of the given equation is 0 and −2.

Sum of the zeros is 0+(−2)=−2.

Product of the zeros is 0×−2=0.

According to the given equation,

The sum of the zeros is,

a

−b

=

4

−(8)

=−2

The product of the zeros is,

a

c

=

4

0

=0

Hence, it is verified that,

sumofzeros=

coefficientofx

2

−coefficientofx

And,

productofzeros=

coefficientofx

2

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