the sum and productof the zeros of the quadritic polynomials are 3 and -10 respectively. what is the quadritic polynomial is?
Answers
Answer:
Sum of zeroes/roots = 3
Product of zeroes/roots = -10
Since quadratic polynomial can be written as,
x² - (sum of roots)x + (product of roots)
Therefore required quadratic polynomial will be,
x² - 3x - 10
EXPLANATION.
Sum of the zeroes of the quadratic polynomial = 3.
Products of the zeroes of the quadratic polynomial = - 10.
As we know that,
Sum of the zeroes of the quadratic polynomial.
⇒ α + β = - b/a.
⇒ α + β = 3. - - - - - (1).
Products of the zeroes of the quadratic polynomial.
⇒ αβ = c/a.
⇒ αβ = - 10. - - - - - (2).
As we know that,
Formula of the quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (3)x + (-10).
⇒ x² - 3x - 10.
MORE INFORMATION.
Conjugate roots.
(1) = If D < 0.
One roots = α + iβ.
Other roots = α - iβ.
(2) = If D > 0.
One roots = α + √β.
Other roots = α - √β.