find a quadratic polynomial if the zeroes of it are 2 and-1 respectively
Answers
EXPLANATION.
Quadratic polynomial.
Its zeroes are = 2 and - 1.
As we know that,
Let one zeroes be = α = 2.
Other zeroes be = β = - 1.
Sum of the zeroes of the quadratic polynomial.
⇒ α + β = - b/a.
⇒ 2 + (-1) = 1.
⇒ α + β = 1.
Products of the zeroes of the quadratic polynomial.
⇒ αβ = c/a.
⇒ (2)(-1) = - 2.
⇒ αβ = - 2.
As we know that,
Formula of the quadratic polynomial.
⇒ x² - (α + β)x + αβ.
Put the values in the equation, we get.
⇒ x² - (1)x + (-2).
⇒ x² - x - 2.
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.
x² - x - 2
Step-by-step explanation:
Given -
Find a quadratic polynomial, if the zeroes of it are 2 and -1 respectively.
Solution -
We know that,
sum of zeroes = -b/a
product of zeroes = c/a
sum of zeroes = 2 + (-1)
= 2-1
= 1
product of zeroes = 2 × (-1)
= -2
formula To find out the polynomial,
x² - (sum of zeroes)x + (product of zeroes)
=> x² - (1)x + (-2)
=> x² - x - 2
Hence the qua quadratic polynomial is x² - x - 2.
hope it helps.