If m and n are the zeroes of a quadratic polynomial x2 + x – 2 then find the value of 1/m +1/n*
Answers
EXPLANATION.
m and n are the zeroes of the quadratic polynomial.
⇒ x² + x - 2.
As we know that,
Sum of the zeroes of the quadratic equation.
⇒ α + β = -b/a.
⇒ m + n = -1.
Products of the zeroes of the quadratic equation.
⇒ αβ = c/a.
⇒ mn = -2.
To find :
⇒ 1/m + 1/n.
⇒ n + m/mn.
Put the values in the equation, we get.
⇒ -1/-2 = 1/2.
MORE INFORMATION.
Nature of the roots of the quadratic expression.
(1) = Real and unequal, if b² - 4ac > 0.
(2) = Rational and unequal, if b² - 4ac is a perfect square.
(3) = Real and equal, if b² - 4ac = 0.
(4) = If D < 0 Roots are imaginary and unequal Or complex conjugate.
Given ,
The quadratic polynomial is x² - x - 2 and m and n are its zeroes
By prime factorisation method :
x² - x + 2x - 2 = 0
x(x - 1) + 2(x - 1) = 0
(x - 1)(x + 2) = 0
x = 1 or x = -2
Thus ,
1/m + 1/n = 1/1 - 1/2 = 1/2
Hence , the required answer is 1/2