If 1, -2 & 3 are roots of x3 -2x2 +ax+6=0 then find ‘a’
Answers
EXPLANATION.
1, -2 and 3 are roots of cubic equation.
⇒ x³ - 2x² + ax + 6 = 0.
As we know that,
Let, α, β and γ are the roots of cubic equation.
Sum of the zeroes of the cubic polynomial.
⇒ α + β + γ = - b/a.
Products of the zeroes of the cubic polynomial two at the time.
⇒ αβ + βγ + γα = c/a.
Products of the zeroes of the cubic polynomial.
⇒ αβγ = - d/a.
Now, 1, -2 and 3 are the roots of the cubic polynomial.
Sum of the zeroes of the cubic polynomial.
⇒ 1 + (-2) + 3.
⇒ 4 - 2 = 2.
⇒ 2 = - b/a.
Products of the zeroes of the cubic polynomial two at the time.
⇒ (1)(-2) + (-2)(3) + (3)(1).
⇒ - 2 - 6 + 3.
⇒ - 8 + 3 = - 5.
⇒ - 5 = c/a.
Products of the zeroes of the cubic polynomial.
⇒ (1)(-2)(3).
⇒ - 6 = - d/a.
To find : The value of a.
⇒ - 5 = c/a.
⇒ - 5 = a/1.
⇒ a = - 5.
∴ The value of a is - 5.