Question

Find the zeroes of the quadratic polynomial P(x) = 7x² – 5x – 2 and also
verify the relationship between zeroes and coefficients.​

Answer 1

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Step-by-step explanation:

Given quadratic polynomial is 7y

2 − 311

y− 32

.

= 31 (21y 2 −11y−2)

= 31(21y 2−14y+3y−2)

= 31 [7y(3y−2)+(3y−2)]

= 31(3y−2)(7y+1)

y= 32

, y=− 71

The zeroes of the polynomials are,

3

2

, − 71

Relationship between the zeroes and the coefficients of the polynomials-

Sum of the zeros=-

coefficient of y

2

coefficient of y

=− ⎝⎜⎜⎜⎛7− 311

⎠⎟⎟⎟⎞

= 2111

Also sum of zeroes= 32 +(− 71)

= 2114−3

= 2111

Product of the zeroes =

coefficient of y

2

constant term

= 7− 32

= 21−2

Also the product of the zeroes= 32 ×(− 71 )= 21−2