Math, asked by samukchamraxe, 5 hours ago

Find the zeroes of the quadratic polynomial 7 2 − 11 3 − 2 3 and verify the relationship between the zeroes and their coefficients.​

Answers

Answered by hudaattar123
1

Answer:

Given quadratic polynomial is 7y

2

3

11

y−

3

2

.

=

3

1

(21y

2

−11y−2)

=

3

1

(21y

2

−14y+3y−2)

=

3

1

[7y(3y−2)+(3y−2)]

=

3

1

(3y−2)(7y+1)

y=

3

2

, y=−

7

1

The zeroes of the polynomials are,

3

2

, −

7

1

Relationship between the zeroes and the coefficients of the polynomials-

Sum of the zeros=-

coefficient of y

2

coefficient of y

=−

7

3

11

=

21

11

Also sum of zeroes=

3

2

+(−

7

1

)

=

21

14−3

=

21

11

Product of the zeroes =

coefficient of y

2

constant term

=

7

3

2

=

21

−2

Also the product of the zeroes=

3

2

×(−

7

1

)=

21

−2

Hence verified.

Option B is correct

Answered by shrutisharma07
0

Step-by-step explanation:

Given,

q(y) = 7y2 – (11/3)y – 2/3

We put q(y) = 0

⇒ 7y2 – (11/3)y – 2/3 = 0

⇒ (21y2 – 11y -2)/3 = 0

⇒ 21y2 – 11y – 2 = 0

⇒ 21y2 – 14y + 3y – 2 = 0

⇒ 7y(3y – 2) – 1(3y + 2) = 0

⇒ (3y – 2)(7y + 1) = 0

This gives us 2 zeros, for

y = 2/3 and y = -1/7

Hence, the zeros of the quadratic equation are 2/3 and -1/7.

Now, for verification

Sum of zeros = – coefficient of y / coefficient of y2

2/3 + (-1/7) = – (-11/3) / 7

-11/21 = -11/21

Product of roots = constant / coefficient of y2

2/3 x (-1/7) = (-2/3) / 7

– 2/21 = -2/21

Therefore, the relationship between zeros and their coefficients is verified.

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