Find zegoes of puly x+5x-14. Also
venify the relátionship between zerdes
Answers
Answer :
⇒ The zeroes of the polynomial are 2 and -7
Given :
◘ Polynomial, x² + 5x - 14
To find :
◘ Zeroes of the polynomial.
◘ Relationship between zeroes and coefficients.
Solution :
Let's find the zeroes of the given polynomial by factorizing it.
x² + 5x - 14 = 0
x² - 2x + 7x - 14 = 0
x(x - 2) + 7(x - 2) = 0
(x - 2) (x + 7) = 0
⇒ (x - 2) = 0
x = 2
⇒ (x + 7) = 0
x = -7
The zeroes of the polynomial are 2 and -7.
RELATIONSHIP BETWEEN ZEROES AND COEFFICIENTS :
- The given polynomial is x² + 5x - 14
- x² coefficient = 1
x coefficient = 5
constant term = -14
‣‣‣ Sum of zeroes = 2 + (-7)
= 2 - 7
= -5
= -5/1
= [ -x coefficient ]/x² coefficient
‣‣‣ Product of zeroes = 2 × (-7)
= -14
= -14/1
= constant term/x² coefficient
‣‣ HOPE IT HELPS..!