Question

find zeroes of the p(x) = 2x^2-7x+6 and Viryfy the relation between zeros and coefficient? please anyone answer ​

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.

6x

2

−3−7x

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ANSWER

Let f(x)=6x

2

−3−7x

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

6x

2

−7x−3=0

6x

2

−9x+2x−3=0

3x(2x−3)+1(2x−3)=0

(3x+1)(2x−3)=0

x=−

3

1

,x=

2

3

The zeros of the given equation is −

3

1

and

2

3

.

Sum of the zeros is −

3

1

+

2

3

=

6

7

.

Product of the zeros is −

3

1

×

2

3

=−

2

1

.

According to the given equation

The sum of the zeros is,

a

−b

=

6

−(−7)

=

6

7

The product of the zeros is

a

c

=

6

−3

=−

2

1

Hence, it is verified that,

sumofzeros=

coefficientofx

2

−coefficientofx

And,

productofzeros=

coefficientofx

2

constantterm

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